On matrix representation of some finite groups
Abstract
A homomorphism T:g→T(g) of G into GL(M) is a representation of G with representation space M. Two representations T and T' with space M and M' are said to be equivalent if there exists a K-isomorphism S of M and M'. The notation (M:K) is the dimension of M over K where M is a vector space and K is a field while G is a finite group. A matrix representation of G of degree n is a homomorphism T:g→T(g) of G into GL(n, K), where GL(n, K) stands for the group of invertible n × n matrices over K. In this paper, the matrix representations for dihedral groups of order 12 and order 16 and an alternating group of order 12 are presented.
- Publication:
-
Research in Mathematical Sciences: A Catalyst for Creativity and Innovation
- Pub Date:
- April 2013
- DOI:
- 10.1063/1.4801246
- Bibcode:
- 2013AIPC.1522.1055M
- Keywords:
-
- group theory;
- matrix algebra;
- vectors;
- 02.10.Ud;
- 02.10.Yn;
- 02.20.-a;
- Linear algebra;
- Matrix theory;
- Group theory