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

Abstract

In this paper we provide a rigorous proof for the fact that there are exactly 8 connected Alexander quandles of order <TEX>$2^5$</TEX> 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.