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pro vyhledávání: '"Vasil’ev, A. V."'
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
Autor:
Vasil'ev, Andrey V., Gorshkov, Ilya B.
Publikováno v:
Algebra Logic, vol. 62, no. 1, 94-99 (2023)
The question on connection between the structure of a finite group $G$ and the properties of the indices of elements of $G$ has been a popular research topic for many years. The $p$-index $|x^G|_p$ of an element $x$ of a group $G$ is the $p$-part of
Externí odkaz:
http://arxiv.org/abs/2301.09265
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
Publikováno v:
Archiv der Mathematik (Basel), 121, no. 1 (2023), 11--21
Let $\mathfrak{X}$ be a class of finite groups closed under subgroups, homomorphic images, and extensions. We study the question which goes back to the lectures of H. Wielandt in 1963-64: For a given $\mathfrak{X}$-subgroup $K$ and maximal $\mathfrak
Externí odkaz:
http://arxiv.org/abs/2206.10267