BLOCKS WITH NORMAL ABELIAN DEFECT AND ABELIAN p′ INERTIAL QUOTIENT
نویسندگان
چکیده
منابع مشابه
On blocks with abelian defect groups of small rank
Let B be a p-block of a finite group with abelian defect group D. Suppose that D has no elementary abelian direct summand of order p. Then we show that B satisfies Brauer’s k(B)-Conjecture (i. e. k(B) ≤ |D|). Together with former results, it follows that Brauer’s k(B)-Conjecture holds for all blocks of defect at most 3. We also obtain some related results.
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Let G be a nite group and k an algebraically closed eld of characteristic p > 0. If B is a block of the group algebra kG with defect group D, the Brauer correspondent of B is a block b of kN G (D). When D is abelian, the blocks B and b, although they are rarely isomorphic or even Morita equivalent, seem to be very closely related. For example, Alperin's Weight Conjecture predicts that they shou...
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ژورنال
عنوان ژورنال: The Quarterly Journal of Mathematics
سال: 2019
ISSN: 0033-5606,1464-3847
DOI: 10.1093/qmathj/haz025