%0 Journal Article
%T SOLVABILITY OF FREE PRODUCTS, CAYLEY GRAPHS AND COMPLEXES
%J Journal of Algebraic Systems
%I Shahrood University of Technology
%Z 2345-5128
%A Mirebrahimi, Hanieh
%A Ghanei, Fatemeh
%D 2013
%\ 09/15/2013
%V 1
%N 1
%P 45-52
%! SOLVABILITY OF FREE PRODUCTS, CAYLEY GRAPHS AND COMPLEXES
%K simplicial complex
%K fundamental group
%K covering space
%K Caley graph
%K solvable group
%R 10.22044/jas.2013.165
%X In this paper, we verify the solvability of free product of finite cyclic groups with topological methods. We use Cayley graphs and Everitt methods to construct suitable 2-complexes corresponding to the presentations of groups and their commutator subgroups. In particular, using these methods, we prove that the commutator subgroup of ${Z}_{m}*{Z}_{n}$ is free of rank $(m-1)(n-1)$ for all $m,n\geq2$
%U https://jas.shahroodut.ac.ir/article_165_76e847bc1b83709351833bc141c00f5a.pdf