Abstract
Let G and G′ be two finite groups, and p be a prime number. k is an algebraically closed field of characteristic p. We denote by b and b′ the block idempotents of G and G′ over k, respectively. We assume that the block algebras kGb and kG′b′ are basically Morita equivalent. Puig and Zhou (2007) proved that the corresponding block algebras of some special subgroups of G and G′ are also basically Morita equivalent. We investigate the relationships between the basic Morita equivalences of two kinds of subgroups of G and G′: We find a module such that its induced module and its restricted module induce the basic Morita equivalences respectively, hence give a precise description of these basic Morita equivalences.
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Hu, X. A note on the basic Morita equivalences. Sci. China Math. 57, 483–490 (2014). https://doi.org/10.1007/s11425-013-4763-1
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DOI: https://doi.org/10.1007/s11425-013-4763-1