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Archiv der Mathematik

, Volume 73, Issue 1, pp 1–10 | Cite as

Hall polynomials and the fixed space of an automorphism of a finite abelian p-group

  • Jason Fulman
Article
  • 33 Downloads

Abstract.

Recent work on Hall polynomials is used to study the fixed space of a random automorphism of a finite abelian p-group. An expression is found for the chance that an automorphism of an abelian p-group of type \(\lambda \) fixes only the identity. A formula is obtained for the chance that a given subgroup H of type \(\nu \) is the fixed space of an automorphism of an abelian p-group of type (kl). There results generalize work of Rudvalis and Shinoda on the fixed space of an element of GL (n, q).

Keywords

Recent Work Hall Polynomial Fixed Space 

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Copyright information

© Birkhäuser Verlag, Basel 1999

Authors and Affiliations

  • Jason Fulman
    • 1
  1. 1.Department of Mathematics, Dardmouth College, 6188 Bradley Hill, Hanover, New Hampshire 03755-3551, USAUSA

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