Attainability of the minimal exponential growth rate for free products of finite cyclic groups

Autor: Alexey Talambutsa
Rok vydání: 2011
Předmět:
Zdroj: Proceedings of the Steklov Institute of Mathematics. 274:289-302
ISSN: 1531-8605
0081-5438
Popis: We consider free products of two finite cyclic groups of orders 2 and n, where n is a prime power. For any such group ℤ2 * ℤn = 〈a, b | a2 = bn = 1〉, we prove that the minimal growth rate αn is attained on the set of generators {a, b} and explicitly write out an integer polynomial whose maximal root is αn. In the cases of n = 3, 4, this result was obtained earlier by A. Mann. We also show that under sufficiently general conditions, the minimal growth rates of a group G and of its central extension \(\tilde G\) coincide and that the attainability of one implies the attainability of the other. As a corollary, the attainability is proved for some cyclic extensions of the above-mentioned free products, in particular, for groups 〈a, b | a2 = bn〉, which are groups of torus knots for odd n.
Databáze: OpenAIRE
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