Subgroups of odd depth—a necessary condition

Sebastian Burciu

Czechoslovak Mathematical Journal (2013)

  • Volume: 63, Issue: 4, page 1039-1048
  • ISSN: 0011-4642

Abstract

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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.

How to cite

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Burciu, Sebastian. "Subgroups of odd depth—a necessary condition." Czechoslovak Mathematical Journal 63.4 (2013): 1039-1048. <http://eudml.org/doc/260761>.

@article{Burciu2013,
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 $\lbrace 0,1\rbrace $-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.},
author = {Burciu, Sebastian},
journal = {Czechoslovak Mathematical Journal},
keywords = {depth of group algebras; finite group; faithful representation; finite groups; group algebras; irreducible constituents; subgroup depths; ring extensions},
language = {eng},
number = {4},
pages = {1039-1048},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Subgroups of odd depth—a necessary condition},
url = {http://eudml.org/doc/260761},
volume = {63},
year = {2013},
}

TY - JOUR
AU - Burciu, Sebastian
TI - Subgroups of odd depth—a necessary condition
JO - Czechoslovak Mathematical Journal
PY - 2013
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 63
IS - 4
SP - 1039
EP - 1048
AB - 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 $\lbrace 0,1\rbrace $-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.
LA - eng
KW - depth of group algebras; finite group; faithful representation; finite groups; group algebras; irreducible constituents; subgroup depths; ring extensions
UR - http://eudml.org/doc/260761
ER -

References

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