FINITE GROUPS WHICH ADMIT A COPRIME AUTOMORPHISM OF PRIME ORDER WHOSE FIXED POINT SET IS A CYCLIC 3-GROUP

1980 ◽  
Vol 31 (2) ◽  
pp. 233-246 ◽  
Author(s):  
B. RICKMAN
Keyword(s):  
Fixed Point ◽  
Finite Groups ◽  
Prime Order ◽  
Fixed Point Set ◽  
Point Set

scholarly journals Finite groups acting on hyperelliptic 3-manifolds

2020 ◽  
Vol 29 (04) ◽  
pp. 2050021
Author(s):  
Mattia Mecchia
Keyword(s):  
Fixed Point ◽  
Simple Group ◽  
Finite Groups ◽  
Prime Power ◽  
Simple Groups ◽  
Fixed Point Set ◽  
Point Set

We consider 3-manifolds admitting the action of an involution such that its space of orbits is homeomorphic to [Formula: see text] Such involutions are called hyperelliptic as the manifolds admitting such an action. We consider finite groups acting on 3-manifolds and containing hyperelliptic involutions whose fixed-point set has [Formula: see text] components. In particular we prove that a simple group containing such an involution is isomorphic to [Formula: see text] for some odd prime power [Formula: see text], or to one of four other small simple groups.

Actions of finite p-groups on homology manifolds

2001 ◽  
Vol 131 (3) ◽  
pp. 473-486 ◽  
Author(s):  
BERNHARD HANKE
Keyword(s):  
Fixed Point ◽  
Cyclic Group ◽  
Prime Order ◽  
Fixed Point Set ◽  
Poincare Duality ◽  
Cohomology Rings ◽  
Duality Space ◽  
Point Set ◽  
Homology Manifolds ◽  
Poincaré Duality Space

Let a cyclic group of odd prime order p act on a ℤ(p)-Poincaré duality space X. We prove a relation between the Witt classes associated to the [ ]p-cohomology rings of the fixed point set of this action and of X. This is applied to show a similar result for actions of finite p-groups on ℤ(p)-homology manifolds.

Fixed-point sets of smooth actions on spheres

2007 ◽  
Vol 1 (1) ◽  
pp. 95-128
Author(s):  
Masaharu Morimoto
Keyword(s):  
Fixed Point ◽  
Finite Groups ◽  
Basic Problem ◽  
Point Sets ◽  
Fixed Point Set ◽  
Surgery Theory ◽  
Smooth Action ◽  
Point Set ◽  
Current Article ◽  
Fixed Point Sets

AbstractGiven a group, it is a basic problem to determine which manifolds can occur as a fixed-point set of a smooth action of this group on a sphere. The current article answers this problem for a family of finite groups including perfect groups and nilpotent Oliver groups. We obtain the answer as an application of a new deleting and inserting theorem which is formulated to delete (or insert) fixed-point sets from (or to) disks with smooth actions of finite groups. One of the keys to the proof is an equivariant interpretation of the surgery theory of S. E. Cappell and J. L. Shaneson, for obtaining homology equivalences.

scholarly journals Multistep Hybrid Extragradient Method for Triple Hierarchical Variational Inequalities

2013 ◽  
Vol 2013 ◽  
pp. 1-17 ◽  
Author(s):  
Zhao-Rong Kong ◽  
Lu-Chuan Ceng ◽  
Qamrul Hasan Ansari ◽  
Chin-Tzong Pang
Keyword(s):  
Fixed Point ◽  
Variational Inequality ◽  
Variational Inequalities ◽  
Variational Inequality Problem ◽  
Extragradient Method ◽  
Fixed Point Set ◽  
Inequality Problem ◽  
Hybrid Extragradient Method ◽  
Point Set ◽  
Hierarchical Variational Inequalities

We consider a triple hierarchical variational inequality problem (THVIP), that is, a variational inequality problem defined over the set of solutions of another variational inequality problem which is defined over the intersection of the fixed point set of a strict pseudocontractive mapping and the solution set of the classical variational inequality problem. Moreover, we propose a multistep hybrid extragradient method to compute the approximate solutions of the THVIP and present the convergence analysis of the sequence generated by the proposed method. We also derive a solution method for solving a system of hierarchical variational inequalities (SHVI), that is, a system of variational inequalities defined over the intersection of the fixed point set of a strict pseudocontractive mapping and the solution set of the classical variational inequality problem. Under very mild conditions, it is proven that the sequence generated by the proposed method converges strongly to a unique solution of the SHVI.

Stein manifolds of nonnegative curvature

2018 ◽  
Vol 18 (3) ◽  
pp. 285-287
Author(s):  
Xiaoyang Chen
Keyword(s):  
Fixed Point ◽  
Sectional Curvature ◽  
Normal Bundle ◽  
Stein Manifold ◽  
Riemannian Metric ◽  
Nonnegative Curvature ◽  
Fixed Point Set ◽  
Nonnegative Sectional Curvature ◽  
Point Set ◽  
Nonempty Compact

AbstractLet X bea Stein manifold with an anti-holomorphic involution τ and nonempty compact fixed point set Xτ. We show that X is diffeomorphic to the normal bundle of Xτ provided that X admits a complete Riemannian metric g of nonnegative sectional curvature such that τ*g = g.

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