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 $m,n\geq2$
Mirebrahimi, H., & Ghanei, F. (2013). SOLVABILITY OF FREE PRODUCTS, CAYLEY GRAPHS AND COMPLEXES. Journal of Algebraic Systems, 1(1), 45-52. doi: 10.22044/jas.2013.165
MLA
Hanieh Mirebrahimi; Fatemeh Ghanei. "SOLVABILITY OF FREE PRODUCTS, CAYLEY GRAPHS AND COMPLEXES", Journal of Algebraic Systems, 1, 1, 2013, 45-52. doi: 10.22044/jas.2013.165
HARVARD
Mirebrahimi, H., Ghanei, F. (2013). 'SOLVABILITY OF FREE PRODUCTS, CAYLEY GRAPHS AND COMPLEXES', Journal of Algebraic Systems, 1(1), pp. 45-52. doi: 10.22044/jas.2013.165
VANCOUVER
Mirebrahimi, H., Ghanei, F. SOLVABILITY OF FREE PRODUCTS, CAYLEY GRAPHS AND COMPLEXES. Journal of Algebraic Systems, 2013; 1(1): 45-52. doi: 10.22044/jas.2013.165
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