Zobrazeno 1 - 10
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pro vyhledávání: '"Felipe Maria"'
A theorem of Z. Arad and E. Fisman establishes that if $A$ and $B$ are two conjugacy classes of a finite group $G$ such that either $AB=A\cup B$ or $AB=A^{-1} \cup B$, then $G$ cannot be non-abelian simple. We demonstrate that, in fact, $\langle A\ra
Externí odkaz:
http://arxiv.org/abs/2410.02393
Let $N$ be a normal subgroup of a finite group $G$. From a result due to Brauer, it can be derived that the character table of $G$ contains square submatrices which are induced by the $G$-conjugacy classes of elements in $N$ and the $G$-orbits of irr
Externí odkaz:
http://arxiv.org/abs/2409.11591
Let $p$ be a prime. In this paper we classify the $p$-structure of those finite $p$-separable groups such that, given any three non-central conjugacy classes of $p$-regular elements, two of them necessarily have coprime lengths.
Externí odkaz:
http://arxiv.org/abs/2408.02818
Landau's theorem on conjugacy classes asserts that there are only finitely many finite groups, up to isomorphism, with exactly $k$ conjugacy classes for any positive integer $k$. We show that, for any positive integers $n$ and $s$, there exists only
Externí odkaz:
http://arxiv.org/abs/2402.06708
Let $G$ be a finite group and $N$ a normal subgroup of $G$. We determine the structure of $N$ when the diameter of the graph associated to the $G$-conjugacy classes contained in $N$ is as large as possible, that is, is equal to three.
Externí odkaz:
http://arxiv.org/abs/2402.06705
Many results have been established that show how the number of conjugacy classes appearing in the product of classes affect the structure of a finite group. The aim of this paper is to show several results about solvability concerning the case in whi
Externí odkaz:
http://arxiv.org/abs/2402.06703
We summarize several results about non-simplicity, solvability and normal structure of finite groups related to the number of conjugacy classes appearing in the product or the power of conjugacy classes. We also collect some problems that have only b
Externí odkaz:
http://arxiv.org/abs/2402.08131
Suppose that $G$ is a finite group and $K$ a non-trivial conjugacy class of $G$ such that $KK^{-1}=1\cup D\cup D^{-1}$ with $D$ a conjugacy class of $G$. We prove that $G$ is not a non-abelian simple group. We also give arithmetical conditions on the
Externí odkaz:
http://arxiv.org/abs/2402.06274
We prove that if a finite group $G$ contains a conjugacy class $K$ whose square is of the form $1 \cup D$, where $D$ is a conjugacy class of $G$, then $\langle K \rangle$ is a solvable proper normal subgroup of $G$ and we completely determine its str
Externí odkaz:
http://arxiv.org/abs/2402.06243
Let $G$ be a finite group and $N$ a normal subgroup of $G$. We determine the structure of $N$ when the graph $\Gamma_G(N)$, which is the graph associated to the conjugacy classes of $G$ contained in $N$, has no triangles and when the graph consists i
Externí odkaz:
http://arxiv.org/abs/2402.06240