Non-Abelian Groups And The Number Of The Group Irreducible Character

The thesis focus on the relationship between the number of irreducible character of a non-abelian finite group G and the structure of the group . It consists of the following two parts.The first part: Let μ(G) be the ratio of the order of a non-abelian finite group G to the number of irreducible character of the group. We establish a relation between μ(G) and the stucture of the group G, and obtain the lower bound of the ratio by the mininal prime divisor of the order and commutator of the group G, and give a necessary and sufficient condition under which this lower bound is attained.The second part: We study the connection between a non-abelian finite p-group G and the number of conjugacy class of it . We also find some more concise relationships between the minor order of a non-abelian finite p-group G and the number of conjugacy class of it .