Relations between quandle extensions and group extensions

초록

In [6] and [7], Joyce and Matveev showed that for given a group G and an automorphism phi, there is a quandle structure on the underlying set of G. When the automorphism is an inner-automorphism by zeta, we denote this quandle structure as (G, Sic(zeta)). In this paper, we show a relationship between group extensions of a group G and quandle extensions of the quandle (G, Sic(zeta)). In fact, there exists a group homomorphism from H-gp(2) (G ; A) to H-q(2) ((G, Sic(zeta)); A). Next, we show a relationship between quandle extensions of a quandle Q and quandle extensions of the quandle on the inner automorphism group of Q. Indeed, there exists a group homomorphism from H-q(2)(Q ; A) to H-q(2) ((Inn(Q), Sic(zeta)); A). Finally, we observe via examples a relationship between extensions of a quandle and extensions of the inner automorphism group of the quandle. (C) 2021 Published by Elsevier Inc.

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