Crossed modules of hypergroups associated with generalized actions

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Hacettepe Journal of Mathematics and Statistics
Volume:45 Issue:3
Crossed modules of hypergroups associated with generalized actions

Crossed modules of hypergroups associated with generalized actions

Authors : Murat ALP, Bijan DAVVAZ

Pages : 663-673

View : 24 | Download : 10

Publication Date : 2016-06-01

Article Type : Research Paper

Abstract :In this article, by using the notion of generalized action, we introduce the concept of crossed module of hypergroups, in the sense of Marty, and its related structures from the light of crossed polymodules. Hypergroups in the sense of Marty are more different than polygroups since they have not identity element or inverse element in general. Examples of crossed modules of hypergroups are originally presented. These examples illustrate the structure and behavior of crossed modules of hypergroups. Moreover, we obtain a crossed module in the sense of Whitehead from a crossed module of hypergroups by applying the notion of fundamental relation.
Keywords : action, crossed module, hypergroup, fundamental relation

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