SOLVABILITY OF FREE PRODUCTS, CAYLEY GRAPHS AND COMPLEXES

Authors

  • Fatemeh Ghanei Department of pure Mathematics, Ferdowsi University of Mashhad, P.O.Box 1159-91775 Mashhad, Iran
  • Hanieh Mirebrahimi Department of pure Mathematics, Ferdowsi University of Mashhad, P.O.Box 1159-91775 Mashhad, Iran
Abstract:

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 $mathbb{Z}_{m}*mathbb{Z}_{n}$ is free of rank $(m-1)(n-1)$ for all $m,ngeq2$

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Journal title

volume 1  issue 1

pages  45- 52

publication date 2013-09-15

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