Subgroups of odd depth—a necessary condition

Title:

Subgroups of odd depth—a necessary condition

Creator:

Burciu, Sebastian

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:b5abe978-fdc9-491b-b729-76768e41bb8c
uuid:b5abe978-fdc9-491b-b729-76768e41bb8c

Subject:

depth of group algebras, finite group, and faithful representation

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

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.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

1039-1048

Source:

Czechoslovak Mathematical Journal | 2013 Volume:63 | Number:4

Harvested from:

CDK

Metadata only:

false