Supported by the National Natural Science Foundation of China(Grant No.11371335)
Let τ be a subgroup functor and H a p-subgroup of a finite group G. Let G= G/H_G and H= H/H_G. We say that H is Φ-τ-supplement in G if G has a subnormal subgroup T and a τ-subgroup S contained in H such that G=H T...
For each finite group E, let O(E) be a binary relation on the set of all subgroups of E. If A and B are subgroups of a finite group G, then we say that the pair (A, B) enjoys the gradewise property (resp., genera...
The research is supported by the NNSF of China (Grant 11371335) and the Natural Science Foundation of Shandong Province (Grant ZR2014AL001), China.
In this paper, we give some new conditions of the existence of Hall subgroups in non-soluble finite groups, and so the famous Hall theorem and Schur-Zassenhaus theorem are generalized.
a NNSF grant of China(Grant#11371335);Wu Wen-TsunKey Laboratory of Mathematics of Chinese Academy of Sciences.Research of the third author is supported by Chinese Academy of Sciences Visiting Professorship for Senior International Scientists(Grant No.2010T2J12).
Letσ={σi|i∈I}be some partition of the set P of all primes and G afinite group.A set H of subgroups of G is said to be a complete Hallσ-set of G ifevery member≠1 of H is a Hallσi-subgroup of G for some i c l and ...
Research was supported by a NSFC(Grant No.11371335).
Let ■ be a non-empty formation of groups,τ a subgroup functor and H a p-subgroup of a finite group G.Let G=G/H_(G) and H=H/H_(G).We say that H is ■_(τ)-s-supplemented in G if for some subgroup T and some τ-subgro...