English

Weak second maximal subgroups in solvable groups

Group Theory 2018-09-25 v2

Abstract

In this paper, we investigate the difference between weak second maximal subgroups and second maximal subgroups. A sufficient and necessary condition is also given to describe such class of groups whose weak second maximal subgroups coincide with its second maximal subgroups(called WSM-groups) under the solvable case. As an application, we show that every non-vanishing element of a solvable WSM-group lies in its Fitting subgroup.

Keywords

Cite

@article{arxiv.1808.02309,
  title  = {Weak second maximal subgroups in solvable groups},
  author = {Hangyang Meng and Xiuyun Guo},
  journal= {arXiv preprint arXiv:1808.02309},
  year   = {2018}
}