On the control of fusion in the local category for the p-block with a minimal nonabelian defect group |
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Authors: | YANG Sheng & GAO Sheng School of Mathematical Sciences Peking University Beijing China |
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Institution: | YANG Sheng & GAO Sheng School of Mathematical Sciences,Peking University,Beijing 100871,China |
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Abstract: | If B is a p-block of a finite group G with a minimal nonabelian defect group D (p is an odd prime number) and (D, b D ) is a Sylow B-subpair of G, then N G (D, b D ) controls B-fusion of G in most cases. This result is of great importance, because we can use it to obtain a complete set of representatives of G-conjugate classes of B-subsections and to calculate the number of ordinary irreducible characters in B. This result is key to the calculation of the structure invariants of the block with a minimal non... |
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