Zobrazeno 1 - 10
of 2 141
pro vyhledávání: '"20D10"'
Autor:
Arushi, Venkataraman, Geetha
Publikováno v:
Bulletin of the Australian Mathematical Society, First View, p1-11, 27 August 2024
We find an upper bound for the number of groups of order $n$ up to isomorphism in the variety $G = A_pA_qA_r$, where $p$, $q$ and $r$ are distinct primes. We also find a bound on the orders and on the number of conjugacy classes of subgroups that are
Externí odkaz:
http://arxiv.org/abs/2409.08586
Autor:
Lewis, Mark L., Monetta, Carmine
This article investigates neighborhoods' sizes in the enhanced power graph (as known as the cyclic graph) associated with a finite group. In particular, we characterize finite $p$-groups with the smallest maximum size for neighborhoods of nontrivial
Externí odkaz:
http://arxiv.org/abs/2408.16545
Autor:
Shi, Jiangtao, Xu, Fanjie
Let $A$ and $G$ be finite groups such that $A$ acts coprimely on $G$ by automorphisms. We provide a complete classification of a finite group $G$ in which every maximal $A$-invariant subgroup containing the normalizer of some $A$-invariant Sylow subg
Externí odkaz:
http://arxiv.org/abs/2408.01249
Autor:
Murashka, Viachaslau I.
For a wide family of formations $\mathfrak{F}$ (which includes Baer-local formations) it is proved that the $ \mathfrak{F}$-hypercenter of a permutation finite group can be computed in polynomial time. In particular, the algorithms for computing the
Externí odkaz:
http://arxiv.org/abs/2407.13606
Autor:
Murashka, Viachaslau I.
For a Baer-local (composition) Fitting formation $\mathfrak{F}$ the polynomial time algorithm for the computation of the $\mathfrak{F}$-radical of a permutation group is suggested. In particular it is showed how one can compute the $\mathfrak{F}$-rad
Externí odkaz:
http://arxiv.org/abs/2407.12720
Let $(G,\{\rho_0, \rho_1, \rho_2\})$ be a string C-group of order $4p^m$ with type $\{k_1, k_2\}$ for $m \geq 2$, $k_1, k_2\geq 3$ and $p$ be an odd prime. Let $P$ be a Sylow $p$-subgroup of $G$. We prove that $G \cong P \rtimes (\mathbb{Z}_2 \times
Externí odkaz:
http://arxiv.org/abs/2407.10388
Autor:
Bera, Sudip
The enhanced power graph of a group G is a graph with vertex set G, where two distinct vertices x and y are adjacent if and only if there exists an element w in G such that both x and y are powers of w. To obtain the proper enhanced power graph, we c
Externí odkaz:
http://arxiv.org/abs/2407.06652
Autor:
Murashka, Viachaslau I.
For a formation $\mathfrak{F}$ of finite groups consider a graph whose vertices are elements of a finite group and two vertices are connected by an edge if and only if they generates non-$\mathfrak{F}$-group as elements of a group. A hereditary forma
Externí odkaz:
http://arxiv.org/abs/2406.18482
Autor:
Murashka, V. I.
L.A. Shemetkov posed a Problem 9.74 in Kourovka Notebook to find all local formations $\mathfrak{F}$ of finite groups such that every finite minimal non-$\mathfrak{F}$-group is either a Schmidt group or a group of prime order. All known solutions to
Externí odkaz:
http://arxiv.org/abs/2405.20257
Autor:
Byott, Nigel P.
Several constructions have been given for families of simple braces, but few examples are known of simple skew braces which are not braces. In this paper, we exhibit the first example of an infinite family of simple skew braces which are not braces a
Externí odkaz:
http://arxiv.org/abs/2405.16154