Abstract:We define a notion of depth for an inclusion of multimatrix algebras B ⊆ A based on a comparison of powers of the inductionrestriction table M (and its transpose matrix). This notion of depth coincides with the depth from [16]. In particular depth 2 extensions coincide with normal extensions as introduced by Rieffel in [20]. For a group extension H ⊂ G a necessary depth n condition is given in terms of the core of H in G. We prove that the subgroup depth of symmetric groups Sn < Sn+1 is 2n − 1. An appendix by … Show more
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