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pro vyhledávání: '"A P, Vasil'ev"'
A complete classification of the multivalued coset groups of order $3$ is given. The proof is based on the classification of rank $3$ groups having regular normal subgroups.
Externí odkaz:
http://arxiv.org/abs/2410.04341
Autor:
Grechkoseeva, M. A., Vasil'ev, A. V.
The spectrum of a finite group is the set of orders of its elements. We are concerned with finite groups having the same spectrum as a direct product of nonabelian simple groups with abelian Sylow $2$-subgroups. For every positive integer $k$, we fin
Externí odkaz:
http://arxiv.org/abs/2409.15873
A rank 3 graph is an orbital graph of a rank 3 permutation group of even order. Despite the classification of rank 3 graphs being complete, see, e.g., Chapter 11 of the recent monograph 'Strongly regular graphs' by Brouwer and Van Maldeghem, the full
Externí odkaz:
http://arxiv.org/abs/2406.04559
Given a permutation group $G$ on a finite set $\Omega$, let $G^{(k)}$ denote the $k$-closure of $G$, that is, the largest permutation group on $\Omega$ having the same orbits in the induced action on $\Omega^k$ as $G$. Recall that a group is $\mathrm
Externí odkaz:
http://arxiv.org/abs/2406.03780
Autor:
Liu, A-Ming, Vasil'ev, Andrey V.
Given a set of primes $\pi$, the $\pi$-index of an element $x$ of a finite group $G$ is the $\pi$-part of the index of the centralizer of $x$ in $G$. If $\pi=\{p\}$ is a singleton, we just say the $p$-index. If the $\pi$-index of $x$ is equal to $p_1
Externí odkaz:
http://arxiv.org/abs/2405.18678
The spectrum of a group is the set of orders of its elements. Finite groups with the same spectra as the direct squares of the finite simple groups with abelian Sylow 2-subgroups are considered. It is proved that the direct square $J_1\times J_1$ of
Externí odkaz:
http://arxiv.org/abs/2312.07907
Autor:
Ponomarenko, Ilia, Vasil'ev, Andrey V.
Publikováno v:
Internat. J. Algebra Comput., vol. 34, no. 1, 137-145 (2024)
Let $m\ge 3$ be an integer. It is proved that the $m$-closure of a given solvable permutation group of degree $n$ can be constructed in time $n^{O(m)}$.
Comment: 7 pages
Comment: 7 pages
Externí odkaz:
http://arxiv.org/abs/2304.02817
The generalized Fitting height $h^*(G)$ of a finite group $G$ is the least number $h$ such that $\mathrm{F}_h^* (G) = G$, where $\mathrm{F}_{(0)}^* (G) = 1$, and $\mathrm{F}_{(i+1)}^*(G)$ is the inverse image of the generalized Fitting subgroup $\mat
Externí odkaz:
http://arxiv.org/abs/2301.02199
Autor:
Alexander Yu Rudenko, Sofia S. Mariasina, Anastasiia K. Bolikhova, Maxim V. Nikulin, Ratislav M. Ozhiganov, Vasiliy G. Vasil’ev, Yuri A. Ikhalaynen, Anastasia L. Khandazhinskaya, Maxim A. Khomutov, Peter V. Sergiev, Alex R. Khomutov, Vladimir I. Polshakov
Publikováno v:
Frontiers in Chemistry, Vol 12 (2024)
S-Adenosyl-l-methionine (SAM)-mediated methylation of biomolecules controls their function and regulates numerous vital intracellular processes. Analogs of SAM with a reporter group in place of the S-methyl group are widely used to study these proces
Externí odkaz:
https://doaj.org/article/77e58f40aa35434d87abbb35bd6ea9be
Publikováno v:
Ann. Mat. Pura Appl., 202, 2699-2714 (2023)
The spectrum of a finite group is the set of its element orders. We give an affirmative answer to Problem 20.58(a) from the Kourovka Notebook proving that for every positive integer $k$, the $k$-th direct power of the simple linear group $L_{n}(2)$ i
Externí odkaz:
http://arxiv.org/abs/2210.13759