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Mathematica Slovaca

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Volume 68, Issue 3

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Growth series of crossed and two-sided crossed products of cyclic groups

Eylem Güzel Karpuz / Esra Kirmizi Çetinalp
Published Online: 2018-05-18 | DOI: https://doi.org/10.1515/ms-2017-0123

Abstract

We recall that the two-sided crossed product of finite cyclic groups is actually a generalization of the crossed product construction of the same type of groups (cf. [10]). In this paper, by considering the crossed and two-sided crossed products obtained from both finite and infinite cyclic groups, we first present the complete rewriting systems and normal forms of elements over crossed products. (We should note that the complete rewriting systems and normal forms of elements over two-sided crossed products have been recently defined in [10]). In the crossed product case, we will consider their presentations that were given in [2]. As a next step, by using the normal forms of elements of these two products, we calculate the growth series of the crossed product of different combinations of finite and infinite cyclic groups as well as the growth series of two-sided crossed product of finite cyclic groups.

MSC 2010: Primary 16S15, 20E22; Secondary 20M05

Keywords: crossed products; rewriting systems; growth series

This work was supported by the Scientific Research Fund of Karamanoğlu Mehmetbey University Project No: 08-YL-15.

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About the article


Received: 2016-02-11

Accepted: 2016-11-02

Published Online: 2018-05-18

Published in Print: 2018-06-26


Citation Information: Mathematica Slovaca, Volume 68, Issue 3, Pages 537–548, ISSN (Online) 1337-2211, ISSN (Print) 0139-9918, DOI: https://doi.org/10.1515/ms-2017-0123.

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[1]
E. K. Çetinalp and E. G. Karpuz
Bulletin of the Iranian Mathematical Society, 2018

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