Crossed modules of hypergroups associated with generalized actions

Year 2016, Volume: 45 Issue: 3, 663 - 673, 01.06.2016

Murat Alp Bijan Davvaz

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

References

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