Abstract:We show that, given an almost-source algebra π΄ of a π-block of a finite group πΊ, then the unit group of π΄ contains a basis stabilized by the left and right multiplicative action of the defect group if and only if, in a sense to be made precise, certain relative multiplicities of local pointed groups are invariant with respect to the fusion system.
We also show that, when πΊ is π-solvable, those two equivalent conditions hold for some almost-source algebra of the given π-block.
One motive lies in the fact… Show more
Set email alert for when this publication receives citations?
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citationsβcitations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.