Abstract
Let G be a finite group, and let B be a p-block of G with defect group D. Let k 0(B) denote the number of ordinary irreducible characters of height 0 in B. In 1984 Olsson proposed a conjecture: \({k_{0}(B)\leqq |D:D'|}\). In this paper, we will verify Olsson’s conjecture in the case that D is metacyclic and p is odd.
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Yang, S. On Olsson’s conjecture for blocks with metacyclic defect groups of odd order. Arch. Math. 96, 401–408 (2011). https://doi.org/10.1007/s00013-011-0251-4
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DOI: https://doi.org/10.1007/s00013-011-0251-4