Wedderburn decomposition of a semisimple group algebra $\mathbb{F}_qG$ from a subalgebra of factor group of $G$

Abstract

In this paper, we derive a condition under which the Wedderburn decomposition of a semisimple group algebra FqG can be deduced from the Wedderburn decomposition of Fq(G/H), where H is a normal subgroup of G having two elements and q = p k for some prime p and k ∈ Z + . In order to complement the abstract theory of the paper, we deduce the Wedderburn decomposition and hence the unit group of semisimple group algebra Fq(A 5 C 4 ), where A 5 C 4 is a non-metabelian group and C 4 is a cyclic group of order 4.

A short note on the Wedderburn components of a semisimple finite group algebra

“…Here t is unknown, F q i , for each i, is an unknown finite extension of F q and n ′ i s are also unknowns. In the subject of semisimple group algebras, deducing the WD is a very important and extensively studied reserach problem (see [1,2,3,4,7,12,13,14,15,16,17,18,19]).…”

Units of the semisimple group algebras FqSL(2,8) and FqSL(2,9)

“…We notice that the difficulty of exactly identifying the unit group of the SGA increases as the size of the group increases. One may refer [15,17] for some of the recent works in this area. Our first goal in determining the unit group is to infer the Wedderburn decomposition (WD) of F q SL(2, 8) and F q SL(2, 9), respectively.…”