Results 11 to 20 of about 192 (34)

On the maximum order of nilpotent transitive permutation groups

, 2014
Given two positive integers n and c, we determine an upper bound, as a function of n and c, for the maximum order of a finite nilpotent transitive group of degree n and nilpotency class at most c.Comment: 14 ...
Crestani, Eleonora, Spiga, Pablo
core   +1 more source

On the Number of Hamiltonian Groups [PDF]

, 2005
Finite hamiltonian groups are counted. The sequence of numbers of all groups of order $n$ all whose subgroups are normal and the sequence of numbers of all groups of order less or equal to $n$ all whose subgroups are normal are presented.Comment: 6 pages,
Horvat, Boris, Jaklič, Gašper, Pisanski, Tomaž   +2 more
core   +1 more source

Permutation groups, partition lattices and block structures

Forum of Mathematics, Sigma
Let G be a finite transitive permutation group on $\Omega $ . The G-invariant partitions form a sublattice of the lattice of all partitions of $\Omega $ , having the further property that all its elements are uniform (that is, have all parts ...
Marina Anagnostopoulou-Merkouri, R. A. Bailey, Peter J. Cameron   +2 more
doaj   +1 more source

On a question of permutation groups acting on the power set

Open Mathematics
In this work, we settle a conjecture about the number of set-orbits of permutation group acting on the power set.
Li Jinbao, Yang Yong, You Mengxi
doaj   +1 more source

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., Praeger, Cheryl E., Schneider, Csaba   +2 more
core   +2 more sources

A bijection from a finite group to the cyclic group with a divisibility property on the element orders

, 2020
This paper proves that there exists a bijection $f$ from a finite group $G$ of order $n$ onto a cyclic group of order $n$ such that for each element $x\in G$ the order of $x$ divides the order of $f(x)$.Comment: The proof has a ...
Amiri, Mohsen
core  

On imprimitive rank 3 permutation groups

, 2011
A classification is given of rank 3 group actions which are quasiprimitive but not primitive. There are two infinite families and a finite number of individual imprimitive examples.
Devillers, Alice, Giudici, Michael, Li, Cai Heng, Pearce, Geoffrey, Praeger, Cheryl E.   +4 more
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Algebraic properties of generalized Rijndael-like ciphers [PDF]

, 2012
We provide conditions under which the set of Rijndael functions considered as permutations of the state space and based on operations of the finite field $\GF (p^k)$ ($p\geq 2$ a prime number) is not closed under functional composition.
B. Scott, Cory, Kevin W. Bombardier, L. Babinkostova, Matthew M. Cole, Thomas A   +5 more
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Non Abelian Bent Functions

, 2011
International audiencePerfect nonlinear functions from a finite group $G$ to another one $H$ are those functions $f: G \rightarrow H$ such that for all nonzero $\alpha \in G$, the derivative $d_{\alpha}f: x \mapsto f(\alpha x) f(x)^{-1}$ is balanced.
Poinsot, Laurent
core   +3 more sources

On residuals of finite groups

, 2017
A theorem of Dolfi, Herzog, Kaplan, and Lev \cite[Thm.~C]{DHKL} asserts that in a finite group with trivial Fitting subgroup, the size of the soluble residual of the group is bounded from below by a certain power of the group order, and that the ...
Aivazidis, Stefanos, Mueller, Thomas
core