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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
Autor:
Vasil'ev, A. F., Vasil'eva, T. I.
Let $t$ be a fixed natural number. A subgroup $H$ of a group $G$ will be called $\mathrm{K}$-$\mathbb{P}_{t}$-subnormal in $G$ if there exists a chain of subgroups $H = H_{0} \leq H_{1} \leq \cdots \leq H_{m-1} \leq H_{m} = G$ such that either $H_{i-
Externí odkaz:
http://arxiv.org/abs/2405.11652
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
Publikováno v:
Религия, церковь, общество, Vol 3, Pp 158-197 (2014)
Ancestral masks (imagines maiorum) played an important role in the public representation of the Roman aristocracy in the Republican epoch, but remained relevant also in the time of Principate. The paper presents an attempt to trace the role of ancest
Externí odkaz:
https://doaj.org/article/b7e7c79332d1485a938e3e766605567d
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