Results 171 to 180 of about 3,682,623 (208)

Multiplying a conjugacy class by its inverse in a finite group

Israel Journal of Mathematics, 2018
Suppose that G is a finite group and K is a non-trivial conjugacy class of G such that KK−1 = 1 ∪ D ∪ D−1 with D a conjugacy class of G. We prove that G is not a non-abelian simple group and we give arithmetical conditions on the class sizes determining ...
A. Beltrán, M. J. Felipe, C. Melchor
semanticscholar   +1 more source

Conjugacy Classes and Class Number

Integers, 2009
AbstractIt is shown that the conjugacy classes of integral matrices with a given irreducible characteristic polynomial is in bijection with the class group of a corresponding order in an algebraic number field.
openaire   +1 more source

Groups with few conjugacy classes

Proceedings of the Edinburgh Mathematical Society, 2011
AbstractLet G be a finite group, let p be a prime divisor of the order of G and let k(G) be the number of conjugacy classes of G. By disregarding at most finitely many non-solvable p-solvable groups G, we have $k(G)\geq2\smash{\sqrt{p-1}}$ with equality if and only if if $\smash{\sqrt{p-1}}$ is an integer, $G=C_{p}\rtimes\smash{C_{\sqrt{p-1}}}$ and CG ...
Héthelyi, László, Horváth, Erzsébet, Keller, Thomas Michael, Maróti, Attila   +3 more
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Conjugacy class numbers and π-subgroups

Pacific Journal of Mathematics, 2021
The number \(l(G)\) of \(p\)-regular classes of a finite group \(G\) is a key invariant in modular representation theory. The main question is wether \(l(G)\) can be bounded by the number of conjugacy classes of some subgroup of \(G\) of order not divisible by \(p\). This would have consequences for the Malle-Robinson \(l(B)\)-conjecture. In this paper,
Malle, Gunter, Navarro, Gabriel, Robinson, Geoffrey R.   +2 more
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COUNTING CONJUGACY CLASSES IN

Bulletin of the Australian Mathematical Society, 2018
We show that if a finitely generated group$G$has a nonelementary WPD action on a hyperbolic metric space$X$, then the number of$G$-conjugacy classes of$X$-loxodromic elements of$G$coming from a ball of radius$R$in the Cayley graph of$G$grows exponentially in$R$.
MICHAEL HULL, ILYA KAPOVICH
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Groups with bounded verbal conjugacy classes

Journal of Group Theory, 2006
Let \(F\) be a free group, \(w\in F\), \(G_w\) be the set of all \(w\)-values in \(G\) and let \(w(G)\) be the verbal subgroup of \(G\) corresponding to \(w\) (i.e., \(w(G)\) is the subgroup generated by \(G_w\)). A word \(w\) is called boundedly concise if, for each group \(G\) such that \(|G_w|\leq m\), we have \(|w(G)|\leq c\) for some integer \(c\)
Brazil, Sergio, Krasilnikov, Alexei, Shumyatsky, Pavel   +2 more
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Frobenius Conjugacy Classes

2012
This chapter analyzes Frobenius conjugacy classes. It shows that in either the split or nonsplit case, when χ‎ is good for N, the conjugacy class FrobE,X has unitary eigenvalues in every representation of the reductive group Garith,N. Now fix a maximal compact subgroup K of the complex reductive group Garith,N (ℂ).
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On a class of selection rules without group actions in field theory and string theory

SciPost Physics
We discuss a class of selection rules which i) do not come from group actions on fields, ii) are exact at tree level in perturbation theory, iii) are increasingly violated as the loop order is raised, and iv) eventually reduce to selection rules ...
Justin Kaidi, Yuji Tachikawa, Hao Zhang
semanticscholar   +1 more source

Commuting Conjugacy Class Graph of Finite CA-Groups

, 2020
M. Salahshour, A. Ashrafi
semanticscholar   +1 more source

Commuting conjugacy class graphs of finite groups

, 2020
M. Salahshour, A. Ashrafi
semanticscholar   +1 more source