The Number Of Homomorphisms Between Two Classes Of Non-Abelian Finite Groups With Order 10p~n And Several Classes Of Non-abelian Finite Groups

The homomorphism number among finite groups is an important quantitative information in the theory of finite groups,with which the structure of finite groups can be further explored.In this dissertation,we will consider the two classes of non-abelian groups with all cycle of Sylow p-subgroups with order 10pn which are not isomorphic to each other H=<a,b|a10=1=bpn,a-lba=br,r(?)1(modpn),r5≡1(modpn),p≡1(mod5)>(where p>5 is prime)and non-abelian group M=<a,b,c|as=b2=cpn=1=[a,c]＝[b,c],b-1ab=a-1>(where p>5 is prime)as research objects,calculate the number of homomorphisms of non-abelian group H and metacyclic group Gm=<x>(?)...