Czechoslovak Mathematical Journal

, Volume 63, Issue 4, pp 1039–1048

Subgroups of odd depth—a necessary condition

Article

Abstract

This paper gives necessary and sufficient conditions for subgroups with trivial core to be of odd depth. We show that a subgroup with trivial core is an odd depth subgroup if and only if certain induced modules from it are faithful. Algebraically this gives a combinatorial condition that has to be satisfied by the subgroups with trivial core in order to be subgroups of a given odd depth. The condition can be expressed as a certain matrix with {0, 1}-entries to have maximal rank. The entries of the matrix correspond to the sizes of the intersections of the subgroup with any of its conjugate.

Keywords

depth of group algebras finite group faithful representation 

MSC 2010

34B16 34C25 

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Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2013

Authors and Affiliations

  1. 1.Inst. of Math. “Simion Stoilow” of the Romanian AcademyBucharestRomania
  2. 2.Faculty of Mathematics and Computer ScienceUniversity of BucharestBucharestRomania

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