Maximal subgroups of finite groups avoiding the elements of a generating set [PDF]
, 2018 We give an elementary proof of the following remark: if G is a finite group and { g1, \u2026 , gd} is a generating set of G of smallest cardinality, then there exists a maximal subgroup M of G such that M 29 { g1, \u2026 , gd} = 05. This result leads us
Lucchini, Andrea, Spiga, Pablo
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A classification of primitive permutation groups with finite stabilizers [PDF]
, 2015 We classify all infinite primitive permutation groups possessing a finite point stabilizer, thus extending the seminal Aschbacher-O'Nan-Scott Theorem to all primitive permutation groups with finite point stabilizers.Comment: Accepted in J.
Aschbacher +14 more
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2-closures of primitive permutation groups of holomorph type
Open Mathematics, 2019 The 2-closure G(2) of a permutation group G on a finite set Ω is the largest subgroup of Sym(Ω) which has the same orbits as G in the induced action on Ω × Ω.
Yu Xue, Pan Jiangmin
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Most primitive groups are full automorphism groups of edge-transitive hypergraphs [PDF]
, 2014 We prove that, for a primitive permutation group G acting on a set of size n, other than the alternating group, the probability that Aut(X,Y^G) = G for a random subset Y of X, tends to 1 as n tends to infinity.
Babai, Laszlo, Cameron, Peter J.
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Wave-Shaped Round Functions and Primitive Groups [PDF]
, 2018 Round functions used as building blocks for iterated block ciphers, both in the case of Substitution-Permutation Networks and Feistel Networks, are often obtained as the composition of different layers which provide confusion and diffusion, and key ...
Aragona, Riccardo +4 more
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Factorizations of finite groups by conjugate subgroups which are solvable or nilpotent [PDF]
, 2015 We consider factorizations of a finite group $G$ into conjugate subgroups, $G=A^{x_{1}}\cdots A^{x_{k}}$ for $A\leq G$ and $x_{1},\ldots ,x_{k}\in G$, where $A$ is nilpotent or solvable.
Garonzi, Martino +3 more
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Orbits of primitive k-homogenous groups on (N − k)-partitions with applications to semigroups [PDF]
, 2017 © 2018 American Mathematical Society. The purpose of this paper is to advance our knowledge of two of the most classic and popular topics in transformation semigroups: automorphisms and the size of minimal generating sets. In order to do this, we examine
Araújo, João +2 more
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Two Generalizations of Homogeneity in Groups with Applications to Regular Semigroups [PDF]
, 2014 Let $X$ be a finite set such that $|X|=n$ and let $i\leq j \leq n$. A group $G\leq \sym$ is said to be $(i,j)$-homogeneous if for every $I,J\subseteq X$, such that $|I|=i$ and $|J|=j$, there exists $g\in G$ such that $Ig\subseteq J$.
Araújo, João, Cameron, Peter J.
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On base sizes for actions of finite classical groups [PDF]
, 2007 Let G be a finite almost simple classical group and let ? be a faithful primitive non-standard G-set. A base for G is a subset B C_ ? whose pointwise stabilizer is trivial; we write b(G) for the minimal size of a base for G.
Burness, Timothy C.
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Transitive simple subgroups of wreath products in product action
, 2003 A transitive simple subgroup of a finite symmetric group is very rarely contained in a full wreath product in product action. All such simple permutation groups are determined in this paper.
Baddeley, Robert W. +2 more
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