Geodesic
Subgroups of odd depth—a necessary condition
Czechoslovak Mathematical Journal, Tome 63 (2013) no. 4, pp. 1039-1048.

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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.
DOI : 10.1007/s10587-013-0070-9
Classification : 34B16, 34C25
Keywords: depth of group algebras; finite group; faithful representation 
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     title = {Subgroups of odd depth{\textemdash}a necessary condition},
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Burciu, Sebastian. Subgroups of odd depth—a necessary condition. Czechoslovak Mathematical Journal, Tome 63 (2013) no. 4, pp. 1039-1048. doi : 10.1007/s10587-013-0070-9. http://geodesic.mathdoc.fr/articles/10.1007/s10587-013-0070-9/

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