Sign conjugacy classes in symmetric groups
نویسنده
چکیده
A special type of conjugacy classes in symmetric groups is studied and used to answer a question about odd-degree irreducible characters.
منابع مشابه
Sign Conjugacy Classes of the Symmetric Groups
A conjugacy class C of a finite group G is a sign conjugacy class if every irreducible character of G takes value 0, 1 or −1 on C. In this paper we classify the sign conjugacy classes of the symmetric groups and thereby verify a conjecture of Olsson.
متن کاملA NOTE ON THE COMMUTING GRAPHS OF A CONJUGACY CLASS IN SYMMETRIC GROUPS
The commuting graph of a group is a graph with vertexes set of a subset of a group and two element are adjacent if they commute. The aim of this paper is to obtain the automorphism group of the commuting graph of a conjugacy class in the symmetric groups. The clique number, coloring number, independent number, and diameter of these graphs are also computed.
متن کاملTHE CONJUGACY ACTION OF Sn AND MODULES INDUCED FROM CENTRALISERS
We study representations related to the conjugacy action of the symmetric group. These arise as sums of submodules induced from centraliser subgroups, and their Frobenius characteristics have elegant descriptions, often as a multiplicity-free sum of power-sum symmetric functions. We describe a general framework in which such representations, and consequently such linear combinations of power-su...
متن کاملSubgroups of the Symmetric Group
We started our research with the intent on answering the following question: can we find a way to calculate all the subgroups of the symmetric group. This is easier said that done, as the number of subgroups for a symmetric group grows quickly with each successive symmetric group. This problem can actually be simplified to finding the subgroup conjugacy classes. So now we have the slightly diff...
متن کاملSome connections between powers of conjugacy classes and degrees of irreducible characters in solvable groups
Let $G$ be a finite group. We say that the derived covering number of $G$ is finite if and only if there exists a positive integer $n$ such that $C^n=G'$ for all non-central conjugacy classes $C$ of $G$. In this paper we characterize solvable groups $G$ in which the derived covering number is finite.
متن کامل