Finite Group Algebras, Unit Groups and Coding Theory

13/10/2017, 14:00 - 15:00 in MAP/0G/018

Leo Creedon, Institute of Technology Sligo


Abstract:

The study of the units of group rings is a relatively mature branch of algebra especially when the coefficient ring has characteristic 0. This difficult problem is often somewhat easier when the coefficient ring is a finite field, although new difficulties arise here (for example the algebra may not be semi-simple). The author will discuss his work on constructing the unit group of finite group algebras and determining their abstract structure. The function sending every element of a group to its inverse can be extended linearly to the group algebra to give an involution. Those units whose inverse equals their involution (the so-called unitary units) form an interesting subgroup of the unit group of a group ring. These will also be discussed and recent applications will be given to coding theory.