International Journal of Contemporary Mathematical Sciences, Volume (2), No (14), Year (2007-3) , Pages (685-691)

Title : Growth sequence of Free product of alternating groups ( Growth sequence of Free product of alternating groups )

Authors: Ahmad Erfanian ,

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For a finitely generated group G, we denote Gn as the direct product of n copies of G. The growth sequence of G is the sequence {d(Gn)}n≥1, where d(Gn) is the minimum number of generators of Gn. In this paper, we investigate the growth sequence of G, when G is the free product of alternating groups. In fact, we prove that d  (An ∗ Am) h(2,An)h(k,Am)  ≤ k +2, for all n, m ≥ 5 and k ≥ 2, where h(2,An) is the maximum number t such that d(At n) = 2 and similarly, h(k,Am) is the maximum number s such that d(As m)= k. Moreover, we will consider the case k = 2 and prove that d((An ∗ Am)t ) = 4, for all 1 ≤ t ≤ h(2,An)h(2,Am) and n,m ≥ 5. We have also confirmed the above results by several examples in find section.

Keywords

, Minimum number of generators, growth sequences, free prod-uct, alternating
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@article{paperid:203361,
author = {Erfanian, Ahmad},
title = {Growth sequence of Free product of alternating groups},
journal = {International Journal of Contemporary Mathematical Sciences},
year = {2007},
volume = {2},
number = {14},
month = {March},
issn = {1312-7586},
pages = {685--691},
numpages = {6},
keywords = {Minimum number of generators; growth sequences; free prod-uct; alternating groups},
}

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%0 Journal Article
%T Growth sequence of Free product of alternating groups
%A Erfanian, Ahmad
%J International Journal of Contemporary Mathematical Sciences
%@ 1312-7586
%D 2007

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