Author: David J Green
Title : Chern classes and extraspecial groups of order $p^5$
Date : 7th June 1995
A presentation is obtained for the Chern subring modulo nilradical of
both extraspecial $p$-groups of order $p^5$, for $p$ an odd prime.
Moreover, it is proved that, for every extraspecial $p$-group of
exponent $p$, the top Chern classes of the irreducible representations
do not generate the Chern subring modulo nilradical. Finally, a
related question about symplectic invariants is discussed, and solved
for $Sp_4 (F_p)$.
The main innovation in this work is to consider extraspecial groups
as central products, and to partition the maximal elementary abelian
subgroups of the central product into those which lift to abelian
subgroups of the corresponding direct product, and those which do not.
1991 Mathematics Subject Classification: 20J06