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http://dx.doi.org/10.7858/eamj.2014.019

REVISIT TO CONNECTED ALEXANDER QUANDLES OF SMALL ORDERS VIA FIXED POINT FREE AUTOMORPHISMS OF FINITE ABELIAN GROUPS

Sim, Hyo-Seob (Department of Applied Mathematics, Pukyong National University)
Song, Hyun-Jong (Department of Applied Mathematics, Pukyong National University)

Publication Information

East Asian mathematical journal / v.30, no.3, 2014 , pp. 293-302 More about this Journal

Abstract

In this paper we provide a rigorous proof for the fact that there are exactly 8 connected Alexander quandles of order $2^5$ by combining properties of fixed point free automorphisms of finite abelian 2-groups and the classification of conjugacy classes of GL(5, 2). Furthermore we verify that six of the eight associated Alexander modules are simple, whereas the other two are semisimple.

Keywords

finite connected quandles; fixed point free automorphisms; conjugacy classes; the general linear groups;

Citations & Related Records

Reference

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