scholarly journals Reduction modulo p of cyclic group actions of order pr

1999 ◽  
Vol 141 (1) ◽  
pp. 37-58
Author(s):  
Keiko Kinugawa ◽  
Masayoshi Miyanishi
Keyword(s):  
Cyclic Group ◽  
Group Actions ◽  
Reduction Modulo ◽  
Modulo P

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 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

scholarly journals Permutations, isotropy and smooth cyclic group actions on definite 4–manifolds

2004 ◽  
Vol 8 (1) ◽  
pp. 475-509 ◽  
Author(s):  
Ian Hambleton ◽  
Mihail Tanase
Keyword(s):  
Cyclic Group ◽  
Group Actions

scholarly journals On the Supersingular Reduction of K3 Surfaces with Complex Multiplication

2018 ◽  
Vol 2020 (20) ◽  
pp. 7306-7346
Author(s):  
Kazuhiro Ito
Keyword(s):  
Comparison Theorem ◽  
Complex Multiplication ◽  
K3 Surfaces ◽  
Explicit Description ◽  
Brauer Group ◽  
K3 Surface ◽  
Good Reduction ◽  
Picard Number ◽  
Reduction Modulo ◽  
Modulo P

Abstract We study the good reduction modulo $p$ of $K3$ surfaces with complex multiplication. If a $K3$ surface with complex multiplication has good reduction, we calculate the Picard number and the height of the formal Brauer group of the reduction. Moreover, if the reduction is supersingular, we calculate its Artin invariant under some assumptions. Our results generalize some results of Shimada for $K3$ surfaces with Picard number $20$. Our methods rely on the main theorem of complex multiplication for $K3$ surfaces by Rizov, an explicit description of the Breuil–Kisin modules associated with Lubin–Tate characters due to Andreatta, Goren, Howard, and Madapusi Pera, and the integral comparison theorem recently established by Bhatt, Morrow, and Scholze.

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