COMMUTATIVE p-SCHUR RINGS OVER NON-ABELIAN GROUPS OF ORDER p3

COMMUTATIVE p-SCHUR RINGS OVER NON-ABELIAN GROUPS OF ORDER p

Recently, it was proved that every p-Schur ring over an abelian group of order p is Schurian. In this paper, we prove that every commutative p-Schur ring over a non-abelian group of order p is Schurian.

Commutative Schur rings over symmetric groups II :

We determine the commutative Schur rings over S6 that contain the sum of all the transpositions in S6. There are eight such types (up to conjugacy), of which four have the set of all the transpositions as a principal set of the Schur ring. 2010 MSC: 20C05, 20F55

THE STRUCTURE OF FINITE ABELIAN p-GROUPS BY THE ORDER OF THEIR SCHUR MULTIPLIERS

A well-known result of Green [4] shows for any finite p-group G of order p^n, there is an integer t(G) , say corank(G), such that |M(G)|=p^(1/2n(n-1)-t(G)) . Classifying all finite p-groups in terms of their corank, is still an open problem. In this paper we classify all finite abelian p-groups by their coranks.  

Chevalley Groups over Commutative Rings

On the commuting graph of non-commutative rings of order $p^nq$

Let $R$ be a non-commutative ring with unity. The commuting graph of $R$ denoted by $Gamma(R)$, is a graph with vertex set $RZ(R)$ and two vertices $a$ and $b$ are adjacent iff $ab=ba$. In this paper, we consider the commuting graph of non-commutative rings of order pq and $p^2q$ with Z(R) = 0 and non-commutative rings with unity of order $p^3q$. It is proved that $C_R(a)$ is a commutative ring...