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pro vyhledávání: '"Vasil'ev, Andrey V."'
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:
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
Publikováno v:
Sib. Math. J. vol. 63, no. 6, 1041-1048 (2022)
We refer to $d(G)$ as the minimal cardinality of a generating set of a finite group $G$, and say that $G$ is $d$-generated if $d(G)\leq d$. A transitive permutation group $G$ is called $\frac{3}{2}$-transitive if a point stabilizer $G_\alpha$ is nont
Externí odkaz:
http://arxiv.org/abs/2202.09705
Publikováno v:
J. Algebr. Comb .57, 227-237 (2023)
A Cayley graph over a group $G$ is said to be central if its connection set is a normal subset of $G$. We prove that every central Cayley graph over a simple group $G$ has at most two pairwise nonequivalent Cayley representations over $G$ associated
Externí odkaz:
http://arxiv.org/abs/2112.05838
Publikováno v:
Commun. Math. Stat. vol.11, 169-194 (2023)
The spectrum of a finite group is the set of element orders of this group. The main goal of this paper is to survey results concerning recognition of finite simple groups by spectrum, in particular, to list all finite simple groups for which the reco
Externí odkaz:
http://arxiv.org/abs/2111.15198