The Number of Fixed Points of Cyclic Group Actions

1984 ◽  
Vol 16 (3) ◽  
pp. 295-302
Author(s):  
John Ewing ◽  
Czes Kosniowski
Keyword(s):  
Fixed Points ◽  
Cyclic Group ◽  
Group Actions

scholarly journals PSL(2, q) as an image of the extended modular group with applications to group actions on surfaces

1987 ◽  
Vol 30 (1) ◽  
pp. 143-151 ◽  
Author(s):  
David Singerman
Keyword(s):  
Free Product ◽  
Cyclic Group ◽  
Modular Group ◽  
Prime Power ◽  
Group Actions ◽  
Index 2 ◽  
Image Position

The modular group PSL(2, ℤ), which is isomorphic to a free product of a cyclicgroupof order 2 and a cyclic group of order 3, has many important homomorphic images. Inparticular, Macbeath [7] showed that PSL(2, q) is an image of the modular group if q ≠ 9. (Here, as usual, q is a prime power.) The extended modular group PGL(2, ℤ) contains PSL{2, ℤ) with index 2. It has a presentationthe subgroup PSL(2, ℤ) being generated by UV and VW.

Maximum orders of cyclic group actions on surfaces extending over the 3-dimensional torus

2017 ◽  
Vol 26 (06) ◽  
pp. 1742005
Author(s):  
Chao Wang ◽  
Shicheng Wang ◽  
Yimu Zhang
Keyword(s):  
Cyclic Group ◽  
Group Actions ◽  
Closed Surface ◽  
Dimensional Torus ◽  
Maximum Order ◽  
3 Dimensional

We determine the maximum order of cyclic group actions on the pair [Formula: see text] among all embeddings of closed surface [Formula: see text] into the 3-dimensional torus [Formula: see text] in the orientable category.

scholarly journals Extended periodic links and HOMFLYPT polynomial

2019 ◽  
Vol 28 (11) ◽  
pp. 1940006
Author(s):  
Nafaa Chbili ◽  
Hajer Jebali
Keyword(s):  
Fixed Points ◽  
Cyclic Group ◽  
Finite Cyclic Group

Extended strongly periodic links have been introduced by Przytycki and Sokolov as a symmetric surgery presentation of three-manifolds on which the finite cyclic group acts without fixed points. The purpose of this paper is to prove that the symmetry of these links is reflected by the first coefficients of the HOMFLYPT polynomial.

On isolated fixed points of group actions on poincaré complexes

Mathematika ◽  
1974 ◽  
Vol 21 (1) ◽  
pp. 114-115 ◽  
Author(s):  
J. P. E. Hodgson
Keyword(s):  
Fixed Points ◽  
Group Actions

scholarly journals Fixed points of discrete nilpotent group actions on $S^2$

2002 ◽  
Vol 52 (4) ◽  
pp. 1075-1091 ◽  
Author(s):  
Suely Druck ◽  
Fuquan Fang ◽  
Sebastião Firmo
Keyword(s):  
Nilpotent Group ◽  
Fixed Points ◽  
Group Actions
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