A finite group G is called a special local 2-nilpotent group if G is not 2-nilpotent,the Sylow 2-subgroup P of G has a section isomorphic to the quaternion group of order 8,Ω(P∩G')≤Z(P)and NG(P)is 2-nilpotent.I...A finite group G is called a special local 2-nilpotent group if G is not 2-nilpotent,the Sylow 2-subgroup P of G has a section isomorphic to the quaternion group of order 8,Ω(P∩G')≤Z(P)and NG(P)is 2-nilpotent.In this paper,it is shown that SL2(q),q>3,is a special local 2-nilpotent group if and only if q^2≡1(mod 16),and that GL2(q),q>3,is a special local 2-nilpotent group if and only if q is odd.Moreover,the solvability of finite groups is also investigated by giving two generalizations of a result from[A note on p-nilpotence and solvability of finite groups,J.Algebra 321(2009)1555-1560].展开更多
For any prime p, all finite noncyclic p-groups which contain a self-centralizing cyclic normal subgroup are determined by using cohomological techniques. Some applications are given, including a character theoretic de...For any prime p, all finite noncyclic p-groups which contain a self-centralizing cyclic normal subgroup are determined by using cohomological techniques. Some applications are given, including a character theoretic description for such groups.展开更多
A finite non-abelian group G is called metahamiltonian if every subgroup of G is either abelian or normal in G.If G is non-nilpotent,then the structure of G has been determined.If G is nilpotent,then the structure of ...A finite non-abelian group G is called metahamiltonian if every subgroup of G is either abelian or normal in G.If G is non-nilpotent,then the structure of G has been determined.If G is nilpotent,then the structure of G is determined by the structure of its Sylow subgroups.However,the classification of finite metahamiltonian p-groups is an unsolved problem.In this paper,finite metahamiltonian p-groups are completely classified up to isomorphism.展开更多
Let G be a finite nonabelian group which has no abelian maximal subgroups and satisfies that any two non-commutative elements generate a maximal subgroup. Then G is isomorphic to the smallest Suzuki 2-group of order 64.
Group sparse residual constraint with non-local priors(GSRC)has achieved great success in image restoration producing stateof-the-art performance.In the GSRC model,the l_(1)norm minimization is employed to reduce the ...Group sparse residual constraint with non-local priors(GSRC)has achieved great success in image restoration producing stateof-the-art performance.In the GSRC model,the l_(1)norm minimization is employed to reduce the group sparse residual.In recent years,nonconvex regularization terms have been widely used in image denoising problems,which have achieved better results in denoising than convex regularization terms.In this paper,we use the ratio of the l_(1)and l_(2)norm instead of the l_(1)norm to propose a new image denoising model,i.e.,a group sparse residual constraint model with l_(1)/l_(2)minimization(GSRC-l_(1)/l_(2)).Due to the computational difficulties arisen from the non-convexity and non-linearity,we focus on a constrained optimization problem that can be solved by alternative direction method of multipliers(ADMM).Experimental results of image denoising show that the pro-posed model outperforms several state-of-the-art image denoising methods both visually and quantitatively.展开更多
基金Shandong Provincial Natural Science Foundation,China(ZR2017MA022)NSFC(11561021 and 11761079)+3 种基金Slovenian Research Agency(research program P1-0285research projects N1-0038,N1-0062,J1-6720,J1-6743,J1-7051,J1-9110)in part by NSFC(11561021)NSFC(11201403 and 11561021).
文摘A finite group G is called a special local 2-nilpotent group if G is not 2-nilpotent,the Sylow 2-subgroup P of G has a section isomorphic to the quaternion group of order 8,Ω(P∩G')≤Z(P)and NG(P)is 2-nilpotent.In this paper,it is shown that SL2(q),q>3,is a special local 2-nilpotent group if and only if q^2≡1(mod 16),and that GL2(q),q>3,is a special local 2-nilpotent group if and only if q is odd.Moreover,the solvability of finite groups is also investigated by giving two generalizations of a result from[A note on p-nilpotence and solvability of finite groups,J.Algebra 321(2009)1555-1560].
基金Supported by the NSF of China(11171194)by the NSF of Shanxi Province(2012011001-1)
文摘For any prime p, all finite noncyclic p-groups which contain a self-centralizing cyclic normal subgroup are determined by using cohomological techniques. Some applications are given, including a character theoretic description for such groups.
基金This work was supported by NSFC(Nos.11971280,11771258).
文摘A finite non-abelian group G is called metahamiltonian if every subgroup of G is either abelian or normal in G.If G is non-nilpotent,then the structure of G has been determined.If G is nilpotent,then the structure of G is determined by the structure of its Sylow subgroups.However,the classification of finite metahamiltonian p-groups is an unsolved problem.In this paper,finite metahamiltonian p-groups are completely classified up to isomorphism.
基金NSFC (No.10671114)NSF of Shanxi Province (No.20051007)the Returned Overseas(student) Fund of Shanxi province (No.[2007]13-56)
文摘Let G be a finite nonabelian group which has no abelian maximal subgroups and satisfies that any two non-commutative elements generate a maximal subgroup. Then G is isomorphic to the smallest Suzuki 2-group of order 64.
基金Supported by the Open Fund of Key Laboratory of Anhui Higher Education Institutes(CS2021-07)the National Natural Science Foundation of China(61701004),the Outstanding Young Talents Support Program of Anhui Province(GXYQ 2021178)University Natural Science Research Project of Anhui Province of China(KJ2020A0238)。
文摘Group sparse residual constraint with non-local priors(GSRC)has achieved great success in image restoration producing stateof-the-art performance.In the GSRC model,the l_(1)norm minimization is employed to reduce the group sparse residual.In recent years,nonconvex regularization terms have been widely used in image denoising problems,which have achieved better results in denoising than convex regularization terms.In this paper,we use the ratio of the l_(1)and l_(2)norm instead of the l_(1)norm to propose a new image denoising model,i.e.,a group sparse residual constraint model with l_(1)/l_(2)minimization(GSRC-l_(1)/l_(2)).Due to the computational difficulties arisen from the non-convexity and non-linearity,we focus on a constrained optimization problem that can be solved by alternative direction method of multipliers(ADMM).Experimental results of image denoising show that the pro-posed model outperforms several state-of-the-art image denoising methods both visually and quantitatively.
