East Asian mathematical journal

The Youngnam Mathematical Society (영남수학회)
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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)
  • Received : 2013.12.27
  • Accepted : 2014.02.25
  • Published : 2014.05.31
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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.

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References

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