The Number of Conjugacy Classes and Irreducible Characters in a Finite Group

Author:

Aja Remigius Okeke,Obasi Uchenna Emmanuel,Eze Everestus Obinwanne

Abstract

In this paper, number of conjugacy classes and irreducible characters in a non-abelian group of order $2^6$ are investigated using cycle pattern of elements. Through the exploits of commutator and representation of elements as a product of disjoint cycles, the number of conjugacy classes is obtained which extends some results in literature.

Publisher

Earthline Publishers

Reference7 articles.

1. Attila Maróti, Bounding the number of conjugacy classes of a permutation group, School of Mathematics and Statistics, University of Birmingham, UK, 2004, pp. 1-12.

2. L. G. Kovacs and G. R. Robinson, On the number of conjugacy classes of a finite group, Journal of Algebra 160(2) (1993), 441-460. https://doi.org/10.1006/jabr.1993.1196

3. I. J. Ugbene, E. O. Eze and S. O. Makanjuola, On the number of conjugacy classes in the injective order decreasing transformation semigroup, Pacific Journal of Science and Technology 14(1) (2013), 182-186.

4. A. Mann, Conjugacy classes in finite groups, Israel Journal of Mathematics 31 (1978), 78-84. https://doi.org/10.1007/BF02761381

5. A. V. Lopez, Conjugacy classes in finite solvable groups, Israel Journal of Mathematics 47 (1984), 241-245. https://doi.org/10.1007/BF02760519

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