Automorphism groups of in nite meta-(locally cyclic) groups

2011 ◽  
Vol 41 (7) ◽  
pp. 613-628 ◽  
Author(s):  
HeGuo LIU ◽  
Jun LIAO
Keyword(s):  
Automorphism Groups ◽  
Cyclic Groups

scholarly journals Serre’s Property (FA) for automorphism groups of free products

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Naomi Andrew
Keyword(s):  
Automorphism Group ◽  
Free Product ◽  
Finite Groups ◽  
Automorphism Groups ◽  
Sufficient Conditions ◽  
Free Products ◽  
Cyclic Groups ◽  
Link Type ◽  
Open Case

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.

scholarly journals Atomic Latin Squares based on Cyclotomic Orthomorphisms

10.37236/1919 ◽  
2005 ◽  
Vol 12 (1) ◽  
Author(s):  
Ian M. Wanless
Keyword(s):  
Finite Fields ◽  
Complete Graph ◽  
Prime Order ◽  
Automorphism Groups ◽  
Latin Square ◽  
Latin Squares ◽  
Established Method ◽  
Cyclic Groups ◽  
Complete Bipartite Graphs ◽  
First Time

Atomic latin squares have indivisible structure which mimics that of the cyclic groups of prime order. They are related to perfect $1$-factorisations of complete bipartite graphs. Only one example of an atomic latin square of a composite order (namely 27) was previously known. We show that this one example can be generated by an established method of constructing latin squares using cyclotomic orthomorphisms in finite fields. The same method is used in this paper to construct atomic latin squares of composite orders 25, 49, 121, 125, 289, 361, 625, 841, 1369, 1849, 2809, 4489, 24649 and 39601. It is also used to construct many new atomic latin squares of prime order and perfect $1$-factorisations of the complete graph $K_{q+1}$ for many prime powers $q$. As a result, existence of such a factorisation is shown for the first time for $q$ in $\big\{$529, 2809, 4489, 6889, 11449, 11881, 15625, 22201, 24389, 24649, 26569, 29929, 32041, 38809, 44521, 50653, 51529, 52441, 63001, 72361, 76729, 78125, 79507, 103823, 148877, 161051, 205379, 226981, 300763, 357911, 371293, 493039, 571787$\big\}$. We show that latin squares built by the 'orthomorphism method' have large automorphism groups and we discuss conditions under which different orthomorphisms produce isomorphic latin squares. We also introduce an invariant called the train of a latin square, which proves to be useful for distinguishing non-isomorphic examples.

Determination of torsion Abelian groups by their automorphism groups

2003 ◽  
Vol 67 (3) ◽  
pp. 511-519
Author(s):  
P. Schultz ◽  
A. Sebeldin ◽  
A. L. Sylla
Keyword(s):  
Automorphism Group ◽  
Automorphism Groups ◽  
Abelian Groups ◽  
Torsion Group ◽  
Cyclic Component ◽  
Cyclic Groups

An Abelian torsion group is determined by its automorphism group if and only if its locally cyclic component is determined by its automorphism group. We describe the locally cyclic groups that are determined by their automorphism groups.

scholarly journals Automorphism Groups of Rational Circulant Graphs

10.37236/2039 ◽  
2012 ◽  
Vol 19 (1) ◽  
Author(s):  
Mikhail Klin ◽  
István Kovács
Keyword(s):  
Orthogonal Group ◽  
Automorphism Groups ◽  
Cayley Graphs ◽  
Symmetric Groups ◽  
Wreath Products ◽  
Circulant Graphs ◽  
Cyclic Groups ◽  
Block Structures

The paper concerns the automorphism groups of Cayley graphs over cyclic groups which have a rational spectrum (rational circulant graphs for short). With the aid of the techniques of Schur rings it is shown that the problem is equivalent to consider the automorphism groups of orthogonal group block structures of cyclic groups. Using this observation, the required groups are expressed in terms of generalized wreath products of symmetric groups.

scholarly journals On Automorphism Groups of Some Particular Groups

2016 ◽  
Vol 40 (2) ◽  
pp. 109-115
Author(s):  
Mohd Altab Hossain ◽  
Subrata Majumdar
Keyword(s):  
Automorphism Groups ◽  
Additive Group ◽  
Rational Numbers ◽  
Real Numbers ◽  
Cyclic Groups ◽  
Academy Of Sciences

The cyclic groups, the additive group Q of rational numbers and the additive group R of real numbers are sometimes very useful elements in many studies. In this paper, the authors concentrated their intuition in determining the structures of the automorphism groups of these useful groups in the light of previous works.Journal of Bangladesh Academy of Sciences, Vol. 40, No. 2, 109-115, 2016

Algebras with Transitive Automorphism Groups

1986 ◽  
Vol 29 (2) ◽  
pp. 224-226
Author(s):  
L. G. Sweet ◽  
J. A. MacDougall
Keyword(s):  
Automorphism Group ◽  
Direct Product ◽  
Automorphism Groups ◽  
Finite Dimensional Algebra ◽  
Dimensional Algebra ◽  
Transitive Automorphism ◽  
Cyclic Groups ◽  
Finite Dimensional

AbstractLet A be a finite dimensional algebra (not necessarily associative) over a field, whose automorphism group acts transitively. It is shown that K = GF(2) and A is a Kostrikin algebra. The automorphism group is determined to be a semi-direct product of two cyclic groups. The number of such algebras is also calculated.

scholarly journals Cyclic Permutation Groups that are Automorphism Groups of Graphs

2019 ◽  
Vol 35 (6) ◽  
pp. 1405-1432 ◽  
Author(s):  
Mariusz Grech ◽  
Andrzej Kisielewicz
Keyword(s):  
Automorphism Group ◽  
Permutation Group ◽  
Boolean Functions ◽  
Automorphism Groups ◽  
Cyclic Permutation ◽  
Permutation Groups ◽  
Symmetry Groups ◽  
Cyclic Groups

Abstract In this paper we establish conditions for a permutation group generated by a single permutation to be an automorphism group of a graph. This solves the so called concrete version of König’s problem for the case of cyclic groups. We establish also similar conditions for the symmetry groups of other related structures: digraphs, supergraphs, and boolean functions.

scholarly journals Orders of automorphisms of smooth plane curves for the automorphism groups to be cyclic

2021 ◽  
Author(s):  
Taro Hayashi
Keyword(s):  
Automorphism Groups ◽  
Plane Curves ◽  
Fixed Integer ◽  
Cyclic Groups ◽  
Smooth Plane

AbstractFor a fixed integer $$d\ge 4$$ d ≥ 4 , the list of groups that appear as automorphism groups of smooth plane curves whose degree is d is unknown, except for $$d=4$$ d = 4 or 5. Harui showed a certain characteristic about structures of automorphism groups of smooth plane curves. Badr and Bars began to study for certain orders of automorphisms and try to obtain exact structures of automorphism groups of smooth plane curves. In this paper, based on the result of T. Harui, we extend Badr–Bars study for different and new cases, mainly for the cases of cyclic groups that appear as automorphism groups.

Sign in / Sign up

Export Citation Format

Share Document