Results 61 to 70 of about 250,418 (87)

Criteria for the p-solvability and p-supersolvability of finite groups

Mathematical Notes, 2013
A subgroup \(A\) of a finite group \(G\) \textit{covers} the maximal pair \((K,H)\), where \(K\) and \(H\) are subgroups of \(G\) such that \(K\) is a maximal subgroup of \(H\), if \(AH=AK\) and \textit{avoids} \((K,H)\) if \(A\cap K=A\cap H\). Every permutable subgroup covers or avoids every maximal pair, but the converse is not true in general.
Liu, Yufeng, Guo, Wenbin, Kovaleva, V. A., Skiba, A. N.   +3 more
openaire   +1 more source

Notes on Solvability andp-Supersolvability of Finite Groups

Algebra Colloquium, 2019
A subgroup H of G is called ℳ-supplemented in G if there exists a subgroup B of G such that G = HB and HiB < G for every maximal subgroup Hiof H. In this paper, we use ℳ-supplemented subgroups to study the structure of finite groups and obtain some new characterization about solvability and p-supersolvability for a fixed prime p. Some results in the
Jia Zhang, Tingting Qiu, Long Miao, Juping Tang   +3 more
openaire   +1 more source

Groups with fewer than 15 involutions

Communications in Algebra, 2023
We show that if G is a finite group with fewer than 15 involutions, then . We then show that if G contains fewer than 15 involutions such that , then G is a solvable group of 2-rank 1. Furthermore, we show that if G contains involutions and , then G is a
Alireza Khalili Asboei
semanticscholar   +1 more source

On the sum of the inverses of the element orders in finite groups

Communications in Algebra, 2022
Let G be a finite group. Recently various functions are defined related to the set of order elements of G and using these functions, some interesting criteria for solvability, nilpotency, supersolvability and etc., are obtained.
Morteza Baniasad Azad, B. Khosravi, Hamideh Rashidi   +2 more
semanticscholar   +1 more source

Indices of non-supersolvable maximal subgroups in finite groups

Ricerche di Matematica
Two classic results, due to K. Doerk and P. Hall respectively, establish the solvability of those finite groups all of whose maximal subgroups are supersolvable, and the solvability of finite groups in which all maximal subgroups have prime or squared ...
Antonio Beltrán, Changguo Shao
semanticscholar   +1 more source

Basic results on an unsolved problem about factorization of finite groups

, 2021
We deal with an unsolved problem in group theory (question 19.35 of Kourovka Notebook). It asks whether, given a finite group G and a factorization one can always find subsets such that and The case k = 2 is of special interest.
M. Hooshmand
semanticscholar   +1 more source

The semi p-cover-avoidance properties of p-sylowizers in finite groups

, 2021
A subgroup S of G is called a p-sylowizer of a p-subgroup R in G if S is maximal in G with respect to having R as its Sylow p-subgroup. In this paper, we give some new characterizations of p-solvable and p-supersolvable groups by the p-cover-avoidance ...
Xianhua Li, Donglin Lei
semanticscholar   +1 more source

On derived ??-length of a finite ??-solvable group with supersolvable ??-Hall subgroup

2019
It is proved that if ??-Hall subgroup is a supersolvable group then the derived ??-length of a ??-solvable group G is at most 1 + maxr????? l??r(G), where l??r(G) is the derived r-length of a ??-solvable group G.
Monakhov, V.S., Gritsuk, D.V.
openaire   +2 more sources

Detecting structural properties of finite groups by the sum of element orders

Israel Journal of Mathematics, 2019
In this paper, we introduce a new function related to the sum of element orders of finite groups. It is used to give some criteria for a finite group to be cyclic, abelian, nilpotent, supersolvable and solvable, respectively.
Marius Tùarnùauceanu
semanticscholar   +1 more source

On two problems about order sequences of finite groups

Journal of Algebraic Combinatorics
The order sequence of a finite group G is a non-decreasing finite sequence formed of the element orders of G. Several properties of order sequences were studied by P. J. Cameron and H. K. Dey in a recent paper that concludes with a list of open problems.
Mihai-Silviu Lazorec
semanticscholar   +1 more source