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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Detecting the index of a subgroup in the subgroup lattice
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by M. De Falco, F. de Giovanni, C. Musella and R. Schmidt PDF
Proc. Amer. Math. Soc. 133 (2005), 979-985 Request permission

Abstract:

A theorem by Zacher and Rips states that the finiteness of the index of a subgroup can be described in terms of purely lattice-theoretic concepts. On the other hand, it is clear that if $G$ is a group and $H$ is a subgroup of finite index of $G$, the index $|G:H|$ cannot be recognized in the lattice ${\mathfrak {L}}(G)$ of all subgroups of $G$, as for instance all groups of prime order have isomorphic subgroup lattices. The aim of this paper is to give a lattice-theoretic characterization of the number of prime factors (with multiplicity) of $|G:H|$.
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Additional Information
  • M. De Falco
  • Affiliation: Dipartimento di Matematica e Applicazioni, Università di Napoli “Federico II”, Complesso Universitario Monte S. Angelo, Via Cintia, I - 80126 Napoli, Italy
  • Email: mdefalco@unina.it
  • F. de Giovanni
  • Affiliation: Dipartimento di Matematica e Applicazioni, Università di Napoli “Federico II”, Complesso Universitario Monte S. Angelo, Via Cintia, I - 80126 Napoli, Italy
  • Email: degiovan@unina.it
  • C. Musella
  • Affiliation: Dipartimento di Matematica e Applicazioni, Università di Napoli “Federico II”, Complesso Universitario Monte S. Angelo, Via Cintia, I - 80126 Napoli, Italy
  • Email: cmusella@unina.it
  • R. Schmidt
  • Affiliation: Mathematisches Seminar, Universität Kiel, Ludwig-Meyn Straße 4, D - 24098 Kiel, Germany
  • Email: schmidt@math.uni-kiel.de
  • Received by editor(s): October 8, 2003
  • Received by editor(s) in revised form: December 1, 2003
  • Published electronically: September 16, 2004
  • Communicated by: Jonathan I. Hall
  • © Copyright 2004 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 133 (2005), 979-985
  • MSC (2000): Primary 20E15
  • DOI: https://doi.org/10.1090/S0002-9939-04-07638-5
  • MathSciNet review: 2117197