Abstract
AbstractLetpbe a prime,a field ofpnelements, andGa finitep-group. It is shown here that ifGhas a quotient whose commutator subgroup is of orderpand whose centre has indexpk, then the group of normalized units in the group algebrahas a conjugacy class ofpnkelements. This was first proved by A. Bovdi and C. Polcino Milies for the casek= 2; their argument is now generalized and simplified. It remains an intriguing question whether the cardinality of the smallest noncentral conjugacy class can always be recognized from this test.
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