{'fraction_non_alphanumeric': 0.0471584038694075, 'fraction_numerical': 0.0036275695284159614, 'mean_word_length': 4.52, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
The Influence of the Properties of Maximal Subgroups on the Structure of a Finite Group

A subgroup H of a finite group G is called s-seminormal in G if it permuts with every Sylow p-subgroup of G with(p,|H|)=1;a subgroup H of a finite group G is said to be c-supplemented in G if there exists a subgroup N of G such that and H∩N≤HG=CoreG(H).In this paper we prove following:Theorem Let F be a saturated formation containing U,the class of all supersolvable groups and G a group with a normal subgroup H such that G/H∈F.Then G∈F if one of following holds:(1)all maximal subgroups of any Sylow subgroup of H are either s-seminormal or c-supplemented in;(2)all maximal subgroups of all Sylow subgroups of F*(H),the generalized Fitting Subgroup of H,are either s-seminormal or c-supplemented in G.This unifies some recent results.