scholarly journals Some cyclic group actions on a homotopy sphere and the parallelizability of its orbit spaces

1985 ◽  
Vol 21 (4) ◽  
pp. 807-818
Author(s):  
Jin Ho Kwak
Keyword(s):  
Cyclic Group ◽  
Group Actions ◽  
Homotopy Sphere ◽  
Orbit Spaces

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.

On orbit spaces of compact group actions

1982 ◽  
Vol 40 (3-4) ◽  
pp. 209-215
Author(s):  
Satya Deo ◽  
P. Palanichamy
Keyword(s):  
Compact Group ◽  
Group Actions ◽  
Orbit Spaces

scholarly journals ALGEBRAIC REALIZATION FOR CYCLIC GROUP ACTIONS WITH ONE ISOTROPY TYPE

2019 ◽  
Vol 25 (2) ◽  
pp. 483-515
Author(s):  
KARL HEINZ DOVERMANN ◽  
ARTHUR G. WASSERMAN
Keyword(s):  
Cyclic Group ◽  
Group Actions ◽  
Isotropy Type
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