Yıl 2011, Cilt 9, Sayı 9, Sayfalar 133 - 166 2011-06-01
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## ON SUBGROUP DEPTH (WITH AN APPENDIX BY S. DANZ AND B. KULSHAMMER)

#### Sebastian Burciu [1] , Lars Kadison [2] , Burkhard Külshammer [3]

##### 76 97

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.
ring extension, depth, group algebra, Hopf algebra, normal subring, inclusion matrix
Konular JA97UD42EE Makaleler Yazar: Sebastian Burciu Yazar: Lars Kadison Yazar: Burkhard Külshammer
 Bibtex @ { ieja266320, journal = {International Electronic Journal of Algebra}, issn = {1306-6048}, eissn = {1306-6048}, address = {Prof. Dr. Abdullah HARMANCI}, year = {2011}, volume = {9}, pages = {133 - 166}, doi = {}, title = {ON SUBGROUP DEPTH (WITH AN APPENDIX BY S. DANZ AND B. KULSHAMMER)}, key = {cite}, author = {Burciu, Sebastian and Kadison, Lars and Külshammer, Burkhard} } APA Burciu, S , Kadison, L , Külshammer, B . (2011). ON SUBGROUP DEPTH (WITH AN APPENDIX BY S. DANZ AND B. KULSHAMMER). International Electronic Journal of Algebra, 9 (9), 133-166. Retrieved from http://dergipark.gov.tr/ieja/issue/25202/266320 MLA Burciu, S , Kadison, L , Külshammer, B . "ON SUBGROUP DEPTH (WITH AN APPENDIX BY S. DANZ AND B. KULSHAMMER)". International Electronic Journal of Algebra 9 (2011): 133-166 Chicago Burciu, S , Kadison, L , Külshammer, B . "ON SUBGROUP DEPTH (WITH AN APPENDIX BY S. DANZ AND B. KULSHAMMER)". International Electronic Journal of Algebra 9 (2011): 133-166 RIS TY - JOUR T1 - ON SUBGROUP DEPTH (WITH AN APPENDIX BY S. DANZ AND B. KULSHAMMER) AU - Sebastian Burciu , Lars Kadison , Burkhard Külshammer Y1 - 2011 PY - 2011 N1 - DO - T2 - International Electronic Journal of Algebra JF - Journal JO - JOR SP - 133 EP - 166 VL - 9 IS - 9 SN - 1306-6048-1306-6048 M3 - UR - Y2 - 2019 ER - EndNote %0 International Electronic Journal of Algebra ON SUBGROUP DEPTH (WITH AN APPENDIX BY S. DANZ AND B. KULSHAMMER) %A Sebastian Burciu , Lars Kadison , Burkhard Külshammer %T ON SUBGROUP DEPTH (WITH AN APPENDIX BY S. DANZ AND B. KULSHAMMER) %D 2011 %J International Electronic Journal of Algebra %P 1306-6048-1306-6048 %V 9 %N 9 %R %U ISNAD Burciu, Sebastian , Kadison, Lars , Külshammer, Burkhard . "ON SUBGROUP DEPTH (WITH AN APPENDIX BY S. DANZ AND B. KULSHAMMER)". International Electronic Journal of Algebra 9 / 9 (Haziran 2011): 133-166.