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pro vyhledávání: '"Fusari, Marco"'
For a group $G$, a subgroup $U \leq G$ and a group $\mathrm{Inn}(G) \leq A \leq \mathrm{Aut}(G)$, we say that $U$ is an $A$-covering group of $G$ if $G = \bigcup_{a\in A}U^a$. A theorem of Jordan (1872) implies that if $G$ is a finite group, $A = \ma
Externí odkaz:
http://arxiv.org/abs/2410.02569
Autor:
Burness, Timothy C., Fusari, Marco
Let $G \leqslant {\rm Sym}(\Omega)$ be a finite transitive permutation group and recall that an element in $G$ is a derangement if it has no fixed points on $\Omega$. Let $\Delta(G)$ be the set of derangements in $G$ and define $\delta(G) = |\Delta(G
Externí odkaz:
http://arxiv.org/abs/2409.01043
Garonzi and Lucchini~\cite{GL} explored finite groups $G$ possessing a normal $2$-covering, where no proper quotient of $G$ exhibits such a covering. Their investigation offered a comprehensive overview of these groups, delineating that such groups f
Externí odkaz:
http://arxiv.org/abs/2402.14529
Given a permutation group $G$, the derangement graph of $G$ is the Cayley graph with connection set the derangements of $G$. The group $G$ is said to be innately transitive if $G$ has a transitive minimal normal subgroup. Clearly, every primitive gro
Externí odkaz:
http://arxiv.org/abs/2311.05575
Autor:
Fusari, Marco, Spiga, Pablo
Given a finite group $R$, we let $\mathrm{Sub}(R)$ denote the collection of all subgroups of $R$. We show that $|\mathrm{Sub}(R)|< c\cdot |R|^{\frac{\log_2|R|}{4}}$, where $c<7.372$ is an explicit absolute constant. This result is asymptotically best
Externí odkaz:
http://arxiv.org/abs/2304.14200
Publikováno v:
Journal of Group Theory; Sep2024, Vol. 27 Issue 5, p929-965, 37p
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