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Blocks of central -group extensions
Authors:Shigeo Koshitani  Naoko Kunugi
Institution:Department of Mathematics, Faculty of Science, Chiba University, Yayoi-cho, Inage-ku, Chiba, 263-8522, Japan ; Department of Mathematics, Aichi University of Education, Hirosawa, Igaya-cho, Kariya, 448-8542, Japan
Abstract:Let $G$ and $G'$ be finite groups that have a common central $p$-subgroup $Z$ for a prime number $p$, and let ${\overline{A}}$ and ${\overline{A'}}$ respectively be $p$-blocks of $G/Z$ and $G'/Z$ induced by $p$-blocks $A$ and $A'$respectively of $G$ and $G'$, both of which have the same defect group. We prove that if ${\overline{A}}$ and ${\overline{A'}}$ are Morita equivalent via a certain special $({\overline{A}}, {\overline{A'}})$-bimodule, then such a Morita equivalence lifts to a Morita equivalence between $A$ and $A'$.

Keywords:$p$-block  Morita equivalence  central extension
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