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}
}