Results 41 to 50 of about 229,870 (85)

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 Beltr'an, 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

Supersolvable Subgroups of Order Divisible by 3

Results in Mathematics
We determine the structure of the finite non-solvable groups of order divisible by 3 all whose maximal subgroups of order divisible by 3 are supersolvable.
Antonio Beltr'an, Changguo Shao
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

PROPERTIES OF FINITE GROUPS DETERMINED BY THE PRODUCT OF THEIR ELEMENT ORDERS

Bulletin of the Australian Mathematical Society, 2020
For a finite group $G$, define $l(G)=(\prod _{g\in G}o(g))^{1/|G|}/|G|$, where $o(g)$ denotes the order of $g\in G$. We prove that if $l(G)>l(A_{5}),l(G)>l(A_{4}),l(G)>l(S_{3}),l(G)>l(Q_{8})$ or $l(G)>l(C_{2}\times C_{2})$, then $G$ is solvable ...
Morteza Baniasad Azad, B. Khosravi
semanticscholar   +1 more source

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