Results 101 to 110 of about 2,545 (225)

Nilpotency of p-complements and p-regular conjugacy class sizes

, 2007
Let G be a finite p-solvable group. We prove that if the set of conjugacy class sizes of all p′-elements of G is {1,m,pa,mpa}, where m is a positive integer not divisible by p, then the p-complements of G are nilpotent and m is a prime power. This result
Beltrán, Antonio, Felipe, María José
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Group Extensions with Infinite Conjugacy Classes [PDF]

Confluentes Mathematici, 2017
We characterize the group property of being with infinite conjugacy classes (or icc , i.e. infinite and of which all conjugacy classes except { 1
openaire   +3 more sources

Base sizes for simple groups and a conjecture of Cameron [PDF]

, 2009
Let G be a permutation group on a finite set ?. A base for G is a subset B C_ ? whose pointwise stabilizer in G is trivial; we write b(G) for the smallest size of a base for G. In this paper we prove that b(G) ?
Burness, TC, Liebeck, MW, Shalev, A, Liebeck, Martin W., Burness, Timothy C., Shalev, Aner   +5 more
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Counting conjugacy classes and automorphism-conjugacy classes of ZM-groups

Asian-European Journal of Mathematics
In this paper, we count the number of conjugacy and automorphism-conjugacy classes of elements of a ZM-group. The size of a conjugacy class with respect to these two equivalence relations is also counted.
openaire   +2 more sources

Solving Large-Scale Unconstrained Optimization Problems with an Efficient Conjugate Gradient Class

Journal of Mathematics
The main goal of this paper is to introduce an appropriate conjugate gradient class to solve unconstrained optimization problems. The presented class enjoys the benefits of having three free parameters, its directions are descent, and it can fulfill the ...
Sanaz Bojari, Mahmoud Paripour
doaj   +1 more source

Conjugacy classes and growth conditions

Journal of Algebra, 2003
Let \(G\) be a finitely generated group and \(E\) a finite generating system. If \(g\in G\) let \(l_E(g)\) be the minimal length of an expression of \(g\) as a product of elements of \(E\), and let \(f_E(n)\) be the number of elements \(g\) of \(G\) for which \(l_E(G)\leq n\).
openaire   +1 more source

Conjugacy classes and finite p-groups [PDF]

Archiv der Mathematik, 2005
Let $G$ be a finite $p$-group, where $p$ is a prime number, and $a\in G$. Denote by $\Cl(a)=\{gag^{-1}\mid g\in G\}$ the conjugacy class of $a$ in $G$. Assume that $|\Cl(a)|=p^n$. Then $\Cl(a)\Cl(a^{-1})=\{xy\mid x\in \Cl(a), y\in \Cl(a^{-1})\}$ is the union of at least $n(p-1)+1$ distinct conjugacy classes of $G$.
openaire   +2 more sources

Conjugacy class sizes of certain direct products

, 2012
We consider finite groups in which, for all primes p, the p-part of the length of any conjugacy class is trivial or fixed; obtaining a full description in the case in which for each prime divisor p of the order of the group there exists a non-central ...
Casolo, Carlo
core  

The conjugacy class graph of some finite groups and its energy

, 2017
The energy of a graph ?, which is denoted by ? ? , ? ? is defined to be the sum of the absolute values of the eigenvalues of its adjacency matrix. In this paper we present the concepts of conjugacy class graph of dihedral groups and introduce the general
Amirah Afiqah binti Jin Azman
core   +2 more sources

Structure of group invariants of a quasiperiodic flow

Electronic Journal of Differential Equations, 2004
It is shown that the multiplier representation of the generalized symmetry group of a quasiperiodic flow induces a semidirect product structure on certain group invariants (including the generalized symmetry group) of the flow's smooth conjugacy class.
Lennard F. Bakker
doaj