Results 11 to 20 of about 164,822 (269)

On connected components and perfect codes of proper order graphs of finite groups [PDF]

Proceedings of the Estonian Academy of Sciences
Let G be a finite group with the identity element e. The proper order graph of G, denoted by ℒ* (G), is an undirected graph with a vertex set G \ {e}, where two distinct vertices x and y are adjacent whenever o(x) | o(y) or o(y) | o(x), where o(x) and ...
Huani Li, Shixun Lin, Xuanlong Ma
doaj   +1 more source

On the Norm of the Abelian p-Group-Residuals

Mathematics, 2021
Let G be a group. Dp(G)=⋂H≤GNG(H′(p)) is defined and, the properties of Dp(G) are investigated. It is proved that Dp(G)=P[A], where P=D(P) is the Sylow p-subgroup and A=N(A) is a Hall p′-subgroup of Dp(G), respectively.
Baojun Li, Yu Han, Lü Gong, Tong Jiang
doaj   +1 more source

Some criteria for solvability and supersolvability [PDF]

Journal of Mahani Mathematical Research, 2023
Denote by $ G $ a finite group, by  $ {\rm hsn}(G) $ the harmonic mean Sylow number (eliminating the Sylow numbers that are one) in $G$ and by    $ {\rm gsn}(G) $ the geometric mean Sylow number (eliminating the Sylow numbers that are one) in $G$.
Zohreh Habibi, Masoomeh Hezarjaribi
doaj   +1 more source

Convergence of random walks on double transitive group generated by its permutational character

Visnik Harkivsʹkogo Nacionalʹnogo Universitetu im. V.N. Karazina. Cepiâ Matematika, Prikladna Matematika i Mehanika, 2019
Let $P$ be a probability on a finite group $G$, $U(g)=\frac{1}{|G|}$ the uniform (trivial) probability on the group $G$, $P^{(n)}=P *\ldots*P$ an $n$-fold convolution of $P$.
Aleksandr L. Vyshnevetskiy
doaj   +1 more source

A survey on projectively equivalent representations of finite groups [PDF]

Surveys in Mathematics and its Applications, 2020
The paper is a survey type article in which we present some results on projectively equivalent representations of finite groups.
Tania Luminiţa Costache
doaj  

Study of Groups with basic property [PDF]

مجلة جامعة الانبار للعلوم الصرفة, 2012
The purpose of this paper is to study the concept of dependence , independence and the basis of some algebraic structure and give the definition of a finite group with basic property and study some of its basic properties .
Dunia Alawi Jarwan
doaj   +1 more source

On the σ-Length of Maximal Subgroups of Finite σ-Soluble Groups

Mathematics, 2020
Let σ={σi:i∈I} be a partition of the set P of all prime numbers and let G be a finite group. We say that G is σ-primary if all the prime factors of |G| belong to the same member of σ. G is said to be σ-soluble if every chief factor of G is σ-primary, and
Abd El-Rahman Heliel, Mohammed Al-Shomrani, Adolfo Ballester-Bolinches   +2 more
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ENUMERATING FINITE GROUPS

The Quarterly Journal of Mathematics, 1987
This paper deals with the problem of enumerating the number f(n) of isomorphism types of groups of order n. There are three results which give upper bounds for f(n). The first bound holds for arbitrary groups, the second one deals with solvable groups, while the third one applies to groups with abelian Sylow subgroups.
Mciver, A, Neumann, P
openaire   +2 more sources

FINITE GROUPS WITH THE SAME JOIN GRAPH AS A FINITE NILPOTENT GROUP [PDF]

Glasgow Mathematical Journal, 2020
AbstractGiven a finite group G, we denote by Δ(G) the graph whose vertices are the proper subgroups of G and in which two vertices H and K are joined by an edge if and only if G = ⟨H, K⟩. We prove that if there exists a finite nilpotent group X with Δ(G) ≅ Δ(X), then G is supersoluble.
openaire   +4 more sources

Seminormal, Non-Normal Maximal Subgroups and Soluble PST-Groups [PDF]

Advances in Group Theory and Applications, 2016
All groups in this paper are finite. Let G be a group. Maximal subgroups of G are used to establish several new characterisations of soluble PST-groups.
J.C. Beidleman
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