Special Issue in Memory of Sergei Duzhin (1956–2015); Guest Editors: S. V. Chmutov, M. V. Karev, L. H. Kauffman and J. H. PrzytyckiNo Access

Annihilation of torsion in homology of finite $m$ $m$ -AQ quandles

Józef H. Przytycki

Department of Mathematics, The George Washington University, Washington, DC 20052, USA

E-mail Address: przytyck@gwu.edu

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and

Seung Yeop Yang

Department of Mathematics, The George Washington University, Washington, DC 20052, USA

E-mail Address: syyang@gwu.edu

Corresponding author.

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https://doi.org/10.1142/S0218216516420128Cited by:1 (Source: Crossref)

Abstract

It is a classical result in reduced homology of finite groups that the order of a group annihilates its homology. Similarly, we have proved that the torsion subgroup of rack and quandle homology of a finite quasigroup quandle is annihilated by its order. However, it does not hold for connected quandles in general. In this paper, we define an $m$ $m$ -almost quasigroup ( $m$ $m$ -AQ) quandle which is a generalization of a quasigroup quandle and study annihilation of torsion in its rack and quandle homology groups.

Dedicated to memory of Sergei Duzhin (1956–2015)

Keywords:

AMSC: 55N35, 18G60, 57M25

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