Let G be a finite group and H a normal subgroup such that G/H is cyclic. Given a conjugacy class g of G we define its centralizing subgroup to be HCG(g). Let K be such that H ≤ K ≤ G. We show that the G-conjugacy classes contained in K whose centralizing subgroup is K, are equally distributed between the cosets of H in K. The proof of this result is entirely elementary. As an application we fin...

In this work, we study direct limits of finite dimensional basic classical simple Lie superalgebras and obtain the conjugacy classes of Cartan subalgebras under the group of automorphisms.

we say that a finite group $g$ is conjugacy expansive if for anynormal subset $s$ and any conjugacy class $c$ of $g$ the normalset $sc$ consists of at least as many conjugacy classes of $g$ as$s$ does. halasi, mar'oti, sidki, bezerra have shown that a groupis conjugacy expansive if and only if it is a direct product ofconjugacy expansive simple or abelian groups.by considering a character analo...

Let [Formula: see text] be a prime and let the complex field. We explicitly classify finite solvable irreducible monomial subgroups of up to conjugacy. That is, we give complete irredundant list text]-conjugacy class representatives as generating sets matrices. Copious structural information about non-solvable is also proved, enabling classification all such groups bar one family. explain obsta...

Abstract Classical results from the theory of finite soluble groups state that Carter subgroups, i.e. self-normalizing nilpotent coincide with projectors and covering they form a non-empty conjugacy class in groups. This paper presents an extension these facts to $$\pi $$ π -separable groups, for sets primes ...

Abstract We characterize conjugacy classes of isometries odd prime order in unimodular ${\mathbb {Z}}$-lattices. This is applied to give a complete classification non-symplectic automorphisms the known deformation types irreducible holomorphic symplectic manifolds up and birational conjugacy.

Jordan Normal Forms serve as excellent representatives of conjugacy classes matrices over algebraically closed fields. Once we know normal forms, can compute functions matrices, their main invariants, etc. The situation is more complicated if search for forms fields that are not and especially rings.

We introduce a method to explicitly determine the Farrell–Tate cohomology of discrete groups. We apply this method to the Coxeter triangle and tetrahedral groups as well as to the Bianchi groups, i.e. PSL2(O) for O the ring of integers in an imaginary quadratic number field, and to their finite index subgroups. We show that the Farrell–Tate cohomology of the Bianchi groups is completely determi...

‎Let $G $ be a finite group and $X$ be a conjugacy class of $G.$ The‎ ‎rank of $X$ in $G,$ denoted by $rank(G{:}X),$ is defined to‎ ‎be the minimal number of elements of $X$ generating $G.$ In this‎ ‎paper we establish the ranks of all the conjugacy classes of‎ ‎elements for simple alternating group $A_{10}$ using the structure‎ ‎constants method and other results established in‎ ‎[A.B.M‎. ‎Bas...