A note on Olsson%26apos;s Conjecture

作者：Hethelyi Laszlo^*; Kuelshammer Burkhard; Sambale Benjamin

来源：Journal of Algebra, 2014, 398: 364-385.

DOI：10.1016/j.jalgebra.2012.08.010

• Block
• Characters
• Height
• p-Rank
• Defect group
• Subsection

For a p-block B of a finite group G with defect group D Olsson conjectured that k(0)(B) %26lt;= vertical bar D : D%26apos;vertical bar, where k(0)(B) is the number of characters in B of height 0 and D%26apos; denotes the commutator subgroup of D. Brauer deduced Olsson%26apos;s Conjecture in the case where D is a dihedral 2-group using the fact that certain algebraically conjugate subsections are also conjugate in G. We generalize Brauer%26apos;s argument for arbitrary primes p and arbitrary defect groups. This extends two results by Robinson. For p %26gt; 3 we show that Olsson%26apos;s Conjecture is satisfied for defect groups of p-rank 2 and for minimal non-abelian defect groups.

• 出版日期2014-1-15