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Biquandles and multiple conjugation biquandles are algebras which are relatedto links and handlebody-links in $3$-space. Cocycles of them can be used toconstruct state-sum type invariants of links and handlebody-links. In thispaper we discuss cocycles of a certain class of biquandles and multipleconjugation biquandles, which we call $G$-Alexander biquandles and$G$-Alexander multiple conjugation biquandles, with a relationship with groupcocycles. We give a method to obtain a (biquandle or multiple conjugationbiquandle) cocycle of them from a group cocycle.

Cocycles of $G$-Alexander biquandles and $G$-Alexander multiple conjugation biquandles