J. Aust. Math. Soc.
77 (2004), 185189

On the orders of conjugacy classes in group algebras of
pgroups


Abstract

Let p be a prime,
a field of
elements, and G
a finite pgroup. 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.

Download the article in PDF format (size 40 Kb)


