SOLVABILITY OF FREE PRODUCTS, CAYLEY GRAPHS ANDCOMPLEXES

In this paper, we verify the solvability of free product of nite cyclicgroups with topological methods. We use Cayley graphs and Everitt methods to con-struct suitable 2-complexes corresponding to the presentations of groups and theircommutator subgroups. In particular, using these methods, we prove that the com-mutator subgroup of Zm Zn is free of rank (m _ 1)(n _1) for all m; n ? 2.

کلیدواژه ها:

Simplicial complex ، Fundamental group ، Covering space ، Cayley graph ، Solvable group