Automorphism Groups of Countable Structures

AbstractWe provide some necessary and some sufficient conditions for the automorphism group of a free product of (freely indecomposable, not infinite cyclic) groups to have Property (FA). The additional sufficient conditions are all met by finite groups, and so this case is fully characterised. Therefore, this paper generalises the work of N. Leder [Serre’s Property FA for automorphism groups of free products, preprint (2018), https://arxiv.org/abs/1810.06287v1]. for finite cyclic groups, as well as resolving the open case of that paper.

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Steiner triple systems with doubly transitive automorphism groups: A corollary to the classification theorem for finite simple groups

Journal of Combinatorial Theory Series A ◽

10.1016/0097-3165(84)90082-7 ◽

1984 ◽

Vol 36 (1) ◽

pp. 105-110 ◽

Cited By ~ 13

Author(s):

J.D Key ◽

E.E Shult

Keyword(s):

Automorphism Groups ◽

Classification Theorem ◽

Simple Groups ◽

Finite Simple Groups ◽

Steiner Triple Systems ◽

Triple Systems ◽

Transitive Automorphism

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Algebraic varieties with automorphism groups of maximal rank

Mathematische Annalen ◽

10.1007/s00208-012-0783-3 ◽

2012 ◽

Vol 355 (1) ◽

pp. 131-146

Author(s):

De-Qi Zhang

Keyword(s):

Automorphism Groups ◽

Maximal Rank ◽

Algebraic Varieties

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Geometrically rational real conic bundles and very transitive actions

Compositio Mathematica ◽

10.1112/s0010437x10004835 ◽

2010 ◽

Vol 147 (1) ◽

pp. 161-187 ◽

Cited By ~ 6

Author(s):

Jérémy Blanc ◽

Frédéric Mangolte

Keyword(s):

Automorphism Groups ◽

Algebraic Surfaces ◽

Algebraic Models ◽

Transitive Automorphism ◽

Real Locus ◽

Real Algebraic Surfaces ◽

Conic Bundles ◽

Transitive Actions ◽

Insight Into

AbstractIn this article we study the transitivity of the group of automorphisms of real algebraic surfaces. We characterize real algebraic surfaces with very transitive automorphism groups. We give applications to the classification of real algebraic models of compact surfaces: these applications yield new insight into the geometry of the real locus, proving several surprising facts on this geometry. This geometry can be thought of as a half-way point between the biregular and birational geometries.

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STRUCTURED GROUPS AND LINK-HOMOTOPY

Journal of Knot Theory and Its Ramifications ◽

10.1142/s0218216593000040 ◽

1993 ◽

Vol 02 (01) ◽

pp. 37-63 ◽

Cited By ~ 5

Author(s):

JAMES R. HUGHES

Keyword(s):

Automorphism Groups ◽

Original Version ◽

Theoretic Approach ◽

Homotopy Classes ◽

Structure Preserving ◽

Three Sphere ◽

Complex Program ◽

Link Homotopy ◽

Structured Groups

We study link-homotopy classes of links in the three sphere using reduced groups endowed with peripheral structures derived from meridian-longitude pairs. Two types of peripheral structures are considered — Milnor’s original version (called “pre-peripheral structures” in Levine’s terminology) and Levine’s refinement (called simply “peripheral structures”). We show here that pre-peripheral structures are not strong enough to classify links up to link-homotopy, and that Levine’s peripheral structures, although strong enough to distinguish those classes not distinguished by pre-peripheral structures, are also in all likelihood not strong enough to distinguish all link-homotopy classes. Following Levine’s classification program, we compare structure-preserving and realizable automorphisms, using an obstruction-theoretic approach suggested by work of Habegger and Lin. We find that these automorphism groups are in general different, so that a more complex program for classification by structured groups is required.

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