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On the orders of conjugacy classes in group algebras of p-groups
- Part of
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- Journal:
- Journal of the Australian Mathematical Society / Volume 77 / Issue 2 / October 2004
- Published online by Cambridge University Press:
- 09 April 2009, pp. 185-190
- Print publication:
- October 2004
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- Article
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Let p be a prime,
a field of pn 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 pk, then the group of normalized units in the group algebra 
has a conjugacy class of pnk elements. This was first proved by A. Bovdi and C. Polcino Milies for the case k = 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.
a field of 
has a conjugacy class of 