Automorphism Groups of Schur Rings

Automorphism Groups of Schur Rings

In 1993, Muzychuk [18] showed that the rational Schur rings over a cyclic group Zn are in one-to-one correspondence with sublattices of the divisor lattice of n, or equivalently, with sublattices of the lattice of subgroups of Zn. This can easily be extended to show that for any finite group G, sublattices of the lattice of characteristic subgroups of G give rise to rational Schur rings over G ...

Enumeration of Schur Rings Over Small Groups

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

A Graphical Representation of Rings via Automorphism Groups

Let R be a commutative ring with identity. We define a graph ΓAut R(R) on R, with vertices elements of R, such that any two distinct vertices x, y are adjacent if and only if there exists σ ∈ AutR such that σ(x) = y. The idea is to apply graph theory to study orbit spaces of rings under automorphisms. In this article, we define the notion of a ring of type n for n ≥ 0 and characterize all rings...

AUTOMORPHISM GROUP OF GROUPS OF ORDER pqr

H"{o}lder in 1893 characterized all groups of order $pqr$ where  $p>q>r$ are prime numbers. In this paper,  by using new presentations of these groups, we compute their full automorphism group.