solvability of free products, cayley graphs and complexes
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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:
journal of algebraic systemsPublisher: shahrood university of technology
ISSN 2345-5128
volume 1
issue 1 2013
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