Finite groups with smooth one fixed point actions on spheres

1998 ◽  
Vol 10 (4) ◽  
Author(s):  
Erkki Laitinen ◽  
Masaharu Morimoto
Keyword(s):  
Fixed Point ◽  
Finite Groups

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.

A NOTE ON FIXED-POINT-FREE ACTIONS OF FINITE GROUPS

1990 ◽  
Vol 41 (2) ◽  
pp. 127-130 ◽  
Author(s):  
S. D. BELL ◽  
B. HARTLEY
Keyword(s):  
Fixed Point ◽  
Finite Groups ◽  
Free Actions

scholarly journals Superimprimitive 2-generator finite groups

1987 ◽  
Vol 30 (1) ◽  
pp. 103-113
Author(s):  
A. M. Macbeath
Keyword(s):  
Fixed Point ◽  
Finite Groups ◽  
Surface Group

In his thesis, A. A. Hussein Omar, motivated by the study of possible shapes of generic Dirichlet regions for a surface group, made a detailed study for g = 2,3 of the groups generated by pairs (μ, τ) of regular (i.e. fixed-point-free) permutations of order 2,3 respectively and of degree n = 6(2g − 1), such that μ ْ τ is an n-cycle. He observed that, for g = 2,3, precisely one pair generates what he calls a superimprimitive group, and raised the question whether such pairs exist for all g, and, if so, whether they areunique. Our main result is that they do always exist, but that, for large values of g, theyare far from unique. (For details and some motivation for the notation, see [4, 5].)

Finite Groups Admitting a Fixed-Point-Free Automorphism of Order 4

1961 ◽  
Vol 83 (1) ◽  
pp. 71 ◽  
Author(s):  
Daniel Gorenstein ◽  
I. N. Herstein
Keyword(s):  
Fixed Point ◽  
Finite Groups

Inequivalent, bordant group actions on a surface

1986 ◽  
Vol 99 (2) ◽  
pp. 233-238 ◽  
Author(s):  
Charles Livingston
Keyword(s):  
Fixed Point ◽  
Finite Groups ◽  
Group Actions ◽  
Free Actions ◽  
Orientable Surfaces

An action of a group, G, on a surface, F, consists of a homomorphismø: G → Homeo (F).We will restrict our discussion to finite groups acting on closed, connected, orientable surfaces, with ø(g) orientation-preserving for all g ε G. In addition we will consider only effective (ø is injective) free actions. Free means that ø(g) is fixed-point-free for all g ε G, g ≠ 1. This paper addresses the classification of such actions.

scholarly journals Finite groups without fixed-point-free actions on a disk.

1974 ◽  
Vol 20 (4) ◽  
pp. 349-351
Author(s):  
Richard Parris
Keyword(s):  
Fixed Point ◽  
Finite Groups ◽  
Free Actions

scholarly journals Finite groups admitting fixed point free automorphisms of order pq

1987 ◽  
Vol 30 (1) ◽  
pp. 51-56 ◽  
Author(s):  
Cheng Kai-Nah
Keyword(s):  
Fixed Point ◽  
Finite Group ◽  
Finite Groups ◽  
Fitting Height ◽  
A Finite Group

By the results of Rickman [7] and Ralston [6], a finite group G admitting a fixed point free automorphism α of order pq, where p and q are primes, is soluble. If p = q, then |G| is necessarily coprime to |α|, and it follows from Berger [1] that G has Fitting height at most 2, the composition length of <α>. The purpose of this paper is to prove a corresponding result in the case when p≠q.

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