We classify completely three-generator finite p-groups G such that Ф(G)≤Z(G)and|G′|≤p2.This paper is a part of the classification of finite p-groups with a minimal non-abelian subgroup of index p,and solve partly ...We classify completely three-generator finite p-groups G such that Ф(G)≤Z(G)and|G′|≤p2.This paper is a part of the classification of finite p-groups with a minimal non-abelian subgroup of index p,and solve partly a problem proposed by Berkovich.展开更多
By using pronormal minimal subgroups and weak left Engel elements ofprime order of the normalizers of Sylow subgroups of a finite group G, we obtain somesufficient conditions for G to be p-nilpotent, nilpotent and sup...By using pronormal minimal subgroups and weak left Engel elements ofprime order of the normalizers of Sylow subgroups of a finite group G, we obtain somesufficient conditions for G to be p-nilpotent, nilpotent and supersolvable respectively,which generalize some known results.展开更多
We call a subgroup H of a finite group G c-supplemented in G if there exists a subgroup K ofG such that G = HK and H ∩K ≤ core(H). In this paper it is proved that a finite group G is p-nilpotentif G is S4-free and e...We call a subgroup H of a finite group G c-supplemented in G if there exists a subgroup K ofG such that G = HK and H ∩K ≤ core(H). In this paper it is proved that a finite group G is p-nilpotentif G is S4-free and every minimal subgroup of P ∩ GN is c-supplemented in NG(P), and when p = 2 P isquaternion-free, where p is the smallest prime number dividing the order of G, P a Sylow p-subgroup of G.As some applications of this result, some known results are generalized.展开更多
Assume p is an odd prime. We investigate finite p-groups all of whose minimal nonabelian subgroups are of order p^3. Let P1-groups denote the p-groups all of whose minimal nonabelian subgroups are nonme tacyclic of or...Assume p is an odd prime. We investigate finite p-groups all of whose minimal nonabelian subgroups are of order p^3. Let P1-groups denote the p-groups all of whose minimal nonabelian subgroups are nonme tacyclic of order p^3. In this paper, the P1-groups are classified, and as a by-product, we prove the Hughes' conjecture is true for the P1-groups.展开更多
基金supported by National Natural Science Foundation of China (Grant No. 11371232)Natural Science Foundation of Shanxi Province (Grant Nos. 2012011001-3 and 2013011001-1)
文摘We classify completely three-generator finite p-groups G such that Ф(G)≤Z(G)and|G′|≤p2.This paper is a part of the classification of finite p-groups with a minimal non-abelian subgroup of index p,and solve partly a problem proposed by Berkovich.
文摘By using pronormal minimal subgroups and weak left Engel elements ofprime order of the normalizers of Sylow subgroups of a finite group G, we obtain somesufficient conditions for G to be p-nilpotent, nilpotent and supersolvable respectively,which generalize some known results.
基金This work was supported by a research grant of Shanxi Province for the first author and partially supported by a fund of UGC(HK) for the second author (Grant No. 2160126, 1999/2000).
文摘We call a subgroup H of a finite group G c-supplemented in G if there exists a subgroup K ofG such that G = HK and H ∩K ≤ core(H). In this paper it is proved that a finite group G is p-nilpotentif G is S4-free and every minimal subgroup of P ∩ GN is c-supplemented in NG(P), and when p = 2 P isquaternion-free, where p is the smallest prime number dividing the order of G, P a Sylow p-subgroup of G.As some applications of this result, some known results are generalized.
基金Supported by National Natural Science Foundation of China(Grant Nos.11771258 and 11471198)
文摘Assume p is an odd prime. We investigate finite p-groups all of whose minimal nonabelian subgroups are of order p^3. Let P1-groups denote the p-groups all of whose minimal nonabelian subgroups are nonme tacyclic of order p^3. In this paper, the P1-groups are classified, and as a by-product, we prove the Hughes' conjecture is true for the P1-groups.
