Growth series of crossed and two-sided crossed products of cyclic groups
-
Eylem Güzel Karpuz
and
Esra Kirmizi Çetinalp
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.
This work was supported by the Scientific Research Fund of Karamanoğlu Mehmetbey University Project No: 08-YL-15.
Acknowledgement
The authors would like to thank to the referee for his/her kind suggestions and valuable comments that improved the understanding of this paper. The authors would also like to thank Professor A. S. Çevik for his suggestions and enthusiastic encouragement in writing up this paper.
References
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Articles in the same Issue
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- On the solutions of a second-order difference equation in terms of generalized Padovan sequences
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