A subgroup H of a group G is called F-z-supplemented in G if there exists a subgroup K of G, such that G = HK and H∩K≤ Z∞F（G）, where Z∞F（G） is the F-hypercenter of G. We obtain some results about the F-z-suppl...A subgroup H of a group G is called F-z-supplemented in G if there exists a subgroup K of G, such that G = HK and H∩K≤ Z∞F（G）, where Z∞F（G） is the F-hypercenter of G. We obtain some results about the F-z-supplemented subgroups and use them to determine the structure of some groups.展开更多
Theoretical background and an implementation of the p-group generation algorithm by Newman and O’Brien are used to provide computational evidence of a new type of periodically repeating patterns in pruned descendant ...Theoretical background and an implementation of the p-group generation algorithm by Newman and O’Brien are used to provide computational evidence of a new type of periodically repeating patterns in pruned descendant trees of finite p-groups.展开更多
In this paper by techniques of group we give some formulae for solving the general quadratic equations of two variables over a finite field,completely calculate and uniformly deal with the orders of automorphism group...In this paper by techniques of group we give some formulae for solving the general quadratic equations of two variables over a finite field,completely calculate and uniformly deal with the orders of automorphism groups of all p-groups of orders less than p6 under the P Hall's concept of isoclinism,also make a number of corrections for orders of automorphism groups offered for a mistake or fault before.展开更多
A ring R is called clean if every element is the sum of an idempotent and a unit, and R is called uniquely strongly clean （USC for short） if every element is uniquely the sum of an idempotent and a unit that commute...A ring R is called clean if every element is the sum of an idempotent and a unit, and R is called uniquely strongly clean （USC for short） if every element is uniquely the sum of an idempotent and a unit that commute. In this article, some conditions on a ring R and a group G such that RG is clean are given. It is also shown that if G is a locally finite group, then the group ring RG is USC if and only if R is USC, and G is a 2-group. The left uniquely exchange group ring, as a middle ring of the uniquely clean ring and the USC ring, does not possess this property, and so does the uniquely exchange group ring.展开更多
The Paramesotriton caudopunctatus species group is mainly distributed in the karst mountain ecosystems of Guizhou, China. Although some species have been included in previous phylogenetic studies, the evolutionary rel...The Paramesotriton caudopunctatus species group is mainly distributed in the karst mountain ecosystems of Guizhou, China. Although some species have been included in previous phylogenetic studies, the evolutionary relationships and divergence-time of members of this species group as a whole remain unexplored. In this study, we report the sequencing of one protein coding mitochondrial gene fragment(ND2) and one nuclear gene(POMC), and use a combination of phylogenetic analyses and coalescent simulations to explore the cryptic diversity and evolutionary history of the P. caudopunctatus species group. Phylogenetic relationships revealed that the P. caudopunctatus species group is composed of two major groups, i. e., East Clade and Western-South Clade. The divergence-time and ancestral area estimation suggested that the P. caudopunctatus species group likely originated in the Doupeng Mountains in Guizhou, China at 12.34 Ma(95% HPD: 8.30–14.73), and intraspecific divergence began at about 2.17 Ma(95% HPD: 1.39–2.97). This timing coincides with the orogenesis of the Miaoling Mountains during the Late Miocene to early Pleistocene. The delimitation of species in the P. caudopunctatus species group supports the existence of the currently identified species, and consensus was confirmed across methods for the existence of least to two cryptic species within what has been traditionally considered to be P. caudopunctatus species group. This study is of significance for understanding the species formation, dispersal, and diversity of the tailed amphibians in the karst mountains ecosystem of Guizhou and the role of the Miaoling Mountains as a geographical barrier to species dispersal.展开更多
Using the metabelian property, regularity, p-commutativity and some properties of congruence, this paper gave the orders of automorphism groups of family Ф24, which are the groups of order p^6 determined by Rodney Ja...Using the metabelian property, regularity, p-commutativity and some properties of congruence, this paper gave the orders of automorphism groups of family Ф24, which are the groups of order p^6 determined by Rodney James, where p denotes an odd prime.展开更多
Let G be a finite group. A subgroup H of G is called an H-subgroup in G if NG（H）∩ H^g ≤ H for all g C G. A subgroup H of G is called a weakly H-subgroup in G if there exists a normal subgroup K of G such that G = ...Let G be a finite group. A subgroup H of G is called an H-subgroup in G if NG（H）∩ H^g ≤ H for all g C G. A subgroup H of G is called a weakly H-subgroup in G if there exists a normal subgroup K of G such that G = HK and H N K is an H-subgroup in G. In this paper, we investigate the structure of the finite group G under the assumption that every subgroup of G of prime order or of order 4 is a weakly H-subgroup in G. Our results improve and generalize several recent results in the literature.展开更多
AIM: To clarify the effects of the xeroderma pigmentosum group D (XPD) Asp312Asn and Lys751Gln gene polymorphisms on the risk of esophageal cancer (EC).
Let Fq be a finite field of characteristic p (p ≠2) and V4 a four-dimensional Fq-vector space. In this paper, we mainly determine the structure of the transfer ideal for the ring of polynomials Fq[V4] under the actio...Let Fq be a finite field of characteristic p (p ≠2) and V4 a four-dimensional Fq-vector space. In this paper, we mainly determine the structure of the transfer ideal for the ring of polynomials Fq[V4] under the action of a nonmetacyclic p-group P in the modular case. We prove that the height of the transfer ideal is 1 using the fixed point sets of the elements of order p in P and that the transfer ideal is a principal ideal.展开更多
文摘A subgroup H of a group G is called F-z-supplemented in G if there exists a subgroup K of G, such that G = HK and H∩K≤ Z∞F（G）, where Z∞F（G） is the F-hypercenter of G. We obtain some results about the F-z-supplemented subgroups and use them to determine the structure of some groups.
文摘Theoretical background and an implementation of the p-group generation algorithm by Newman and O’Brien are used to provide computational evidence of a new type of periodically repeating patterns in pruned descendant trees of finite p-groups.
基金Supported by the National Natural Science Foundation of China(61074185)Supported by the Projection of Science and Technique for Guangdong Province(2009B030802044)+1 种基金Supported by the Projection of Production,Study and Investigation for Guangdong Province(2010B090301042)Supported by the Science and Study Foundation of Guangxi University(XB2100285)
文摘In this paper by techniques of group we give some formulae for solving the general quadratic equations of two variables over a finite field,completely calculate and uniformly deal with the orders of automorphism groups of all p-groups of orders less than p6 under the P Hall's concept of isoclinism,also make a number of corrections for orders of automorphism groups offered for a mistake or fault before.
文摘A ring R is called clean if every element is the sum of an idempotent and a unit, and R is called uniquely strongly clean （USC for short） if every element is uniquely the sum of an idempotent and a unit that commute. In this article, some conditions on a ring R and a group G such that RG is clean are given. It is also shown that if G is a locally finite group, then the group ring RG is USC if and only if R is USC, and G is a 2-group. The left uniquely exchange group ring, as a middle ring of the uniquely clean ring and the USC ring, does not possess this property, and so does the uniquely exchange group ring.
基金supported by the programs of the Strategic Priority Research Program B of the Chinese Academy of Sciences (CAS) (No. XDB31000000)the National Natural Science Foundation of China (Grant No. 31460091)+2 种基金the Na tional Animal Collection Resource Center, China (Grant No. 2005DKA21402)the Application of Amphibian Natural Antioxidant Peptides as Cosmetic Raw Material Antioxidants (QKZYD [2020]4002)the National Top Discipline Construction Project of Guizhou Province,Geography in Guizhou Normal University (No. 85 2017 Qianjiao Keyan Fa)。
文摘The Paramesotriton caudopunctatus species group is mainly distributed in the karst mountain ecosystems of Guizhou, China. Although some species have been included in previous phylogenetic studies, the evolutionary relationships and divergence-time of members of this species group as a whole remain unexplored. In this study, we report the sequencing of one protein coding mitochondrial gene fragment(ND2) and one nuclear gene(POMC), and use a combination of phylogenetic analyses and coalescent simulations to explore the cryptic diversity and evolutionary history of the P. caudopunctatus species group. Phylogenetic relationships revealed that the P. caudopunctatus species group is composed of two major groups, i. e., East Clade and Western-South Clade. The divergence-time and ancestral area estimation suggested that the P. caudopunctatus species group likely originated in the Doupeng Mountains in Guizhou, China at 12.34 Ma(95% HPD: 8.30–14.73), and intraspecific divergence began at about 2.17 Ma(95% HPD: 1.39–2.97). This timing coincides with the orogenesis of the Miaoling Mountains during the Late Miocene to early Pleistocene. The delimitation of species in the P. caudopunctatus species group supports the existence of the currently identified species, and consensus was confirmed across methods for the existence of least to two cryptic species within what has been traditionally considered to be P. caudopunctatus species group. This study is of significance for understanding the species formation, dispersal, and diversity of the tailed amphibians in the karst mountains ecosystem of Guizhou and the role of the Miaoling Mountains as a geographical barrier to species dispersal.
基金The Science Research Foundation of Chongqing Municipal Education Commission of China(KJ050611)
文摘Using the metabelian property, regularity, p-commutativity and some properties of congruence, this paper gave the orders of automorphism groups of family Ф24, which are the groups of order p^6 determined by Rodney James, where p denotes an odd prime.
基金supported by the Deanship of Scientific Research(DSR) at King Abdulaziz University(KAU) represented by the Unit of Research Groups through the grant number(MG/31/01) for the group entitled "Abstract Algebra and its Applications"
文摘Let G be a finite group. A subgroup H of G is called an H-subgroup in G if NG（H）∩ H^g ≤ H for all g C G. A subgroup H of G is called a weakly H-subgroup in G if there exists a normal subgroup K of G such that G = HK and H N K is an H-subgroup in G. In this paper, we investigate the structure of the finite group G under the assumption that every subgroup of G of prime order or of order 4 is a weakly H-subgroup in G. Our results improve and generalize several recent results in the literature.
文摘AIM: To clarify the effects of the xeroderma pigmentosum group D (XPD) Asp312Asn and Lys751Gln gene polymorphisms on the risk of esophageal cancer (EC).
文摘Let Fq be a finite field of characteristic p (p ≠2) and V4 a four-dimensional Fq-vector space. In this paper, we mainly determine the structure of the transfer ideal for the ring of polynomials Fq[V4] under the action of a nonmetacyclic p-group P in the modular case. We prove that the height of the transfer ideal is 1 using the fixed point sets of the elements of order p in P and that the transfer ideal is a principal ideal.
