On cubic graphical regular representations of finite simple groups

5-Arc transitive cubic Cayley graphs on finite simple groups

In this paper, we determine all connected 5-arc transitive cubic Cayley graphs on the alternating group A47; there are only two such graphs (up to isomorphism). By earlier work of the authors, these are the only two nonnormal connected cubic arc-transitive Cayley graphs for finite nonbelian simple groups, and so this paper completes the classification of such non-normal Cayley graphs.

Disjunctive Identities of Finite Groups and Identities of Regular Representations

The problem of describing identities of concrete algebraic structures is traditionally one of the most attractive in variety theory. Very often it is a difficult problem, and many deep works are entirely devoted to finding bases of identities of classical algebraic objects. This paper was initiated by attempts to find bases of identities for certain representations of finite groups. Let F be th...

Representations of finite groups

A micro-introduction to the theory of representations of finite groups.

On the Regular Power Graph on the Conjugacy Classes of Finite Groups

emph{The (undirected) power graph on the conjugacy classes} $mathcal{P_C}(G)$ of a group $G$ is a simple graph in which the vertices are the conjugacy classes of $G$ and two distinct vertices $C$ and $C'$ are adjacent in $mathcal{P_C}(G)$ if one is a subset of a power of the other. In this paper, we describe groups whose associated graphs are $k$-regular for $k=5,6$.

Representations of Finite Groups