ON THE DIMENSION OF SPHERES WHOSE PRODUCT ADMITS A FREE ACTION BY A NON-ABELIAN GROUP

1985 ◽  
Vol 36 (1) ◽  
pp. 117-127 ◽  
Author(s):  
NOBUAKI YAGITA
Keyword(s):  
Abelian Group ◽  
Free Action

LOCALLY INVARIANT ORDERS ON GROUPS

2006 ◽  
Vol 16 (06) ◽  
pp. 1161-1179 ◽  
Author(s):  
I. M. CHISWELL
Keyword(s):  
Abelian Group ◽  
Fundamental Group ◽  
Recent Work ◽  
Analogous Result ◽  
Hyperbolic Manifold ◽  
Free Groups ◽  
Free Action ◽  
Detailed Proof ◽  
Unique Product ◽  
Invariant Order

Recent work by T. Delzant and S. Hair shows that certain groups are unique product groups. In effect, they show that the groups have a locally invariant order, an idea introduced by D. Promislow in the early eighties. Having a locally invariant order implies the group is a unique product group, and a strict left (or right) ordering on a group is a locally invariant order. We study properties of the class of LIO groups, that is, groups having a locally invariant order. The main result gives conditions under which the fundamental group of a graph of LIO groups is LIO. In particular, the free product of two LIO groups is LIO. There is an analogous result for a graph of right orderable groups. We also study tree-free groups (those having a free action without inversions on a Λ-tree, for some ordered abelian group Λ). In particular, a detailed proof that tree-free groups are LIO is given. There is also a detailed proof of an observation made by Hair, that the fundamental group of a compact hyperbolic manifold is virtually LIO.

Bounding a free action of an abelian group

1974 ◽  
Vol 41 (2) ◽  
pp. 381-385 ◽  
Author(s):  
R. J. Rowlett
Keyword(s):  
Abelian Group ◽  
Free Action

Fixed-point free action of an abelian group of odd non-squarefree exponent

2011 ◽  
Vol 54 (1) ◽  
pp. 77-89 ◽  
Author(s):  
Gülin Ercan ◽  
İsmail Ş. Güloğlu ◽  
Öznur Mut Sağdiçoğlu
Keyword(s):  
Fixed Point ◽  
Finite Group ◽  
Abelian Group ◽  
Solvable Group ◽  
Free Action ◽  
Finite Solvable Group ◽  
Fitting Length ◽  
Point Free Action ◽  
A Finite Group

AbstractLet A be a finite group acting fixed-point freely on a finite (solvable) group G. A longstanding conjecture is that if (|G|, |A|) = 1, then the Fitting length of G is bounded by the length of the longest chain of subgroups of A. It is expected that the conjecture is true when the coprimeness condition is replaced by the assumption that A is nilpotent. We establish the conjecture without the coprimeness condition in the case where A is an abelian group whose order is a product of three odd primes and where the Sylow 2-subgroups of G are abelian.

Minimal Event-Causal Libertarianism

2018 ◽  
Author(s):  
Christopher Evan Franklin
Keyword(s):  
Free Action ◽  
Mental States ◽  
Human Action

This chapter explains the differences between agency reductionism and nonreductionism, explains the varieties of libertarianism, and sets out the main contours of minimal event-causal libertarianism, highlighting just how minimal this theory is. Crucial to understanding how minimal event-causal libertarianism differs from other event-causal libertarian theories is understanding the location and role of indeterminism in human action, the kinds of mental states essential to causing free action, the nature of nondeterministic causation, and how the theory is constructed from compatibilist accounts. The chapter argues that libertarians must face up to both the problem of luck and the problem of enhanced control when determining the best theoretical location of indeterminism.

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