Results 41 to 50 of about 228,002 (82)

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

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

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

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

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

Formations and Products of F(G)-Subnormal Subgroups of Finite Solvable Groups

Mathematical Notes, 2020
A. Vasil'ev, V. I. Murashka
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𝐺-permutable Subgroups in PSL2(𝑞) and Hereditarily 𝐺-permutable Subgroups in PSU3(𝑞)

The Bulletin of Irkutsk State University. Series Mathematics
The concept of 𝑋-permutable subgroup, introduced by A. N. Skiba, generalizes the classical concept of a permutable subgroup. Many classes of finite groups have been characterized in terms of 𝑋-permutable subgroups. In particular, W. Guo, A. N.
A. Galt, V. N. Tyutyanov
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