TY  - JOUR
TT  - ON SUBGROUP DEPTH (WITH AN APPENDIX BY S. DANZ AND B. KULSHAMMER)
AU  - Burciu, Sebastian
AU  - Kadison, Lars
AU  - Külshammer, Burkhard
PY  - 2011
DA  - June
JF  - International Electronic Journal of Algebra
JO  - IEJA
PB  - Abdullah HARMANCI
WT  - DergiPark
SN  - 1306-6048
SP  - 133
EP  - 166
VL  - 9
IS  - 9
KW  - ring extension
KW  - depth
KW  - group algebra
KW  - Hopf algebra
KW  - normal subring
KW  - inclusion matrix
N2  - We define a notion of depth for an inclusion of complex semisimple algebras, based on a comparison of powers of the induction-restriction table (and its transpose matrix) and a previous notion of depth in an earlier paper of the second author. We prove that a depth two extension of complex semisimple algebras is normal in the sense of Rieffel, and conversely. Given an extension H ⊆ G of finite groups we prove that the depth of C H in C G is bounded by 2n if the kernel of the permutation representation of G on cosets of H is the intersection of n conjugate subgroups of H. We prove in several ways that the subgroup depth of symmetric groups Sn ⊆ Sn+1 is 2n − 1. An appendix by S. Danz and B. K¨ulshammer determines the subgroup depth of alternating groups An ⊆ An+1 and dihedral group extensions.
UR  - https://dergipark.org.tr/en/pub/ieja/issue//266320
L1  - https://dergipark.org.tr/en/download/article-file/232843
ER  -