Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2021; 58(5): 1301-1314

Online first article June 3, 2021      Printed September 30, 2021

https://doi.org/10.4134/BKMS.b200961

Copyright © The Korean Mathematical Society.

On the geometry of the crossed product of groups

F\i rat Ate\c{s}, Ahmet Sinan \c{C}evik, Eylem G\"{u}zel Karpuz

Balikesir University; Sel\c{c}uk University; Karamano\u{g}lu Mehmetbey University

Abstract

In this paper, firstly, we work on the presentation of the crossed product of groups of general types. After that we find the generating pictures (Second Homotopy Group) of this product by looking the relations from a geometric viewpoint. Finally, we give some applications.

Keywords: Group presentation, crossed product, $\pi_2$-generators, pictures

MSC numbers: Primary 20F05, 20F55, 20F65

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