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ISSN : 1226-0657

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Vol.25 No.3

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DERIVATION AND ACTOR OF CROSSED POLYMODULES

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2018, v.25 no.3, pp.203-218
https://doi.org/10.7468/jksmeb.2018.25.3.203
Davvaz, Bijan
Alp, Murat
Davvaz,, B. , & Alp,, M. (2018). DERIVATION AND ACTOR OF CROSSED POLYMODULES. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 25(3), 203-218, https://doi.org/10.7468/jksmeb.2018.25.3.203

Abstract

An old result of Whitehead says that the set of derivations of a group with values in a crossed G-module has a natural monoid structure. In this paper we introduce derivation of crossed polymodule and actor crossed polymodules by using Lue's and Norrie's constructions. We prove that the set of derivations of a crossed polygroup has a semihypergroup structure with identity. Then, we consider the polygroup of invertible and reversible elements of it and we obtain actor crossed polymodule.

keywords
action, crossed module, polygroup, crossed polymodule, derivation, fundamental relation

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

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