On Alperin’s Conjecture and Certain Subgroup Complexes
by Külshammer, Burkhard; Robinson, Geoffrey R.
We prove a new formula about local control of the number of p-regular conjugacyclasses of a finite group. We then relate the results to Alperin’s weight conjecture to obtain newresults describing the number of simple modules for a finite group in terms of weights of solvablesubgroups. Finally, we use the results to obtain new formulations of Alperin’s weight conjecture,and to obtain restrictions on the structure of a minimal counterexample.
DOI: 10.1023/A:1009961408896
Print publication date: 12/1/1998
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