JP Journal of Geometry and Topology
Volume 3, Issue 2, Pages 113 - 148
(July 2003)
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THE
LOWER CENTRAL SERIES FOR THE SYMMETRY p-GROUPS
OF A COMPACT ORIENTABLE SURFACE
Reza Zomorrodian (USA)
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Abstract:
Kulkarni
[Topology 26(2) (1987), 195-203] has shown that
there are only three classes of symmetry p-groups
Gp
acting on a compact orientable surface åg
of genus g
³
2. These groups have best upper bounds of 16(g
– 1), 9(g – 1) and 2p(g
– 1)/(p
– 3). These bounds are attained when Gp/åg
@
å0
with branching indices (2, 4, 8) for p
= 2, (3, 3, 9) for p
= 3 and (p,
p, p)
for all p
³
5, respectively. In this paper, we compute the
descending central series for these 3 symmetry p-groups
and explain their relevance to the main
results obtained in [Topology 26(2) (1987),
195-203]. |
| Keywords and phrases: symmetry p-groups, automorphism
groups, surface groups, bounds, lower central series,
torsion free Riemann surfaces, signatures, orbit
genus. |
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