Zobrazeno 1 - 10
of 148
pro vyhledávání: '"Vasil'ev, Andrey A."'
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
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