J. Aust. Math. Soc.
77 (2004), 185-189
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On the orders of conjugacy classes in group algebras of
p-groups
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Abstract
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Let p be a prime,
a field of
 elements, and G
a finite p-group. It is shown here that
if G
has a quotient whose commutator subgroup is of
order p
and whose centre has index
 , then the group of normalized units in the group
algebra 
has a conjugacy class of
 elements. This was first proved by A. Bovdi and
C. Polcino Milies for the case
 ; 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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