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pro vyhledávání: '"Sambale, Benjamin"'
Autor:
Sambale, Benjamin
We give elementary proofs of the following two theorems on automorphisms of a finite group G: (1) An automorphism of G is inner if and only if it extends to an automorphism of every finite group containing G. (2) There exists a finite group, whose ou
Externí odkaz:
http://arxiv.org/abs/2405.02992
Autor:
Sambale, Benjamin
We call a finite group G ultrasolvable if it has a characteristic subgroup series whose factors are cyclic. It was shown by Durbin--McDonald that the automorphism group of an ultrasolvable group is supersolvable. The converse statement was establishe
Externí odkaz:
http://arxiv.org/abs/2403.05926
Autor:
Sambale, Benjamin
We consider complex characters of a p-group P, which are invariant under a fusion system F on P. Extending a theorem of B\'arcenas--Cantarero to non-saturated fusion systems, we show that the number of indecomposable F-invariant characters of P is gr
Externí odkaz:
http://arxiv.org/abs/2401.15706
Autor:
Sambale, Benjamin
Let G be a pi-separable group with a Hall pi-subgroup H or order n. For x in H let lambda(x) be the number of Hall pi-subgroups of G containing x. We show that $\prod_{d\mid n}\prod_{x\in H}\lambda(x^{d})^{\frac{n}{d}\mu(d)}=1$, where mu is the M\"ob
Externí odkaz:
http://arxiv.org/abs/2401.05289
Let $\mathcal{F}$ be a set of finite groups. A finite group $G$ is called an \emph{$\mathcal{F}$-cover} if every group in $\mathcal{F}$ is isomorphic to a subgroup of $G$. An $\mathcal{F}$-cover is called \emph{minimal} if no proper subgroup of $G$ i
Externí odkaz:
http://arxiv.org/abs/2311.15652
Autor:
Sambale, Benjamin
A Sylow p-subgroup P of a finite group G is called redundant if every p-element of G lies in a Sylow subgroup different from P. Generalizing a recent theorem of Mar\'oti--Mart\'inez--Moret\'o, we show that for every non-cyclic p-group P there exists
Externí odkaz:
http://arxiv.org/abs/2311.06931
We classify principal $2$-blocks of finite groups $G$ with Sylow $2$-subgroups isomorphic to a wreathed $2$-group $C_{2^n}\wr C_2$ with $n\geq 2$ up to Morita equivalence and up to splendid Morita equivalence. As a consequence, we obtain that Puig's
Externí odkaz:
http://arxiv.org/abs/2310.13621
Publikováno v:
Journal of Algebraic Combinatorics, 59, Pages 581-595, 2024
Given a finite abelian group $G$ and cyclic subgroups $A$, $B$, $C$ of $G$ of the same order, we find necessary and sufficient conditions for $A$, $B$, $C$ to admit a common transversal for the cosets they afford. For an arbitrary number of cyclic su
Externí odkaz:
http://arxiv.org/abs/2308.06559
Autor:
Sambale, Benjamin
A finite group G with center Z is of central type if there exists a fully ramified character $\lambda\in\mathrm{Irr}(Z)$, i.e. the induced character $\lambda^G$ is a multiple of an irreducible character. Howlett-Isaacs have shown that G is solvable i
Externí odkaz:
http://arxiv.org/abs/2305.19955
Autor:
Sambale, Benjamin
The Frobenius--Schur indicators of characters in a real 2-block with dihedral defect groups have been determined by Murray. We show that two infinite families described in his work do not exist and we construct examples for the remaining families. We
Externí odkaz:
http://arxiv.org/abs/2304.14639