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.

scholarly journals Automorphism groups of smooth plane curves

2019 ◽  
Vol 42 (2) ◽  
pp. 308-331 ◽  
Author(s):  
Takeshi Harui
Keyword(s):  
Automorphism Groups ◽  
Plane Curves ◽  
Smooth Plane

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.

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

Automorphism Groups of Plane Curves

2004 ◽  
Vol 32 (8) ◽  
pp. 2885-2894 ◽  
Author(s):  
Michael J. Bradley ◽  
Harry J. D'Souza
Keyword(s):  
Automorphism Groups ◽  
Plane Curves

Erratum by Editorial office: Quasi-Galois points, I: Automorphism groups of plane curves

2020 ◽  
Vol 72 (1) ◽  
pp. 159-159
Author(s):  
Satoru Fukasawa ◽  
Kei Miura ◽  
Takeshi Takahashi
Keyword(s):  
Automorphism Groups ◽  
Plane Curves ◽  
Editorial Office

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 Lower bounds for Clifford indices in rank three

2010 ◽  
Vol 150 (1) ◽  
pp. 23-33 ◽  
Author(s):  
H. LANGE ◽  
P. E. NEWSTEAD
Keyword(s):  
Lower Bounds ◽  
Vector Bundles ◽  
Plane Curves ◽  
Projective Curve ◽  
Smooth Projective Curve ◽  
Smooth Plane ◽  
Semistable Vector Bundles

AbstractClifford indices for semistable vector bundles on a smooth projective curve of genus at least 4 were defined in previous papers by the authors. In this paper, we establish lower bounds for the Clifford indices for rank 3 bundles. As a consequence we show that, on smooth plane curves of degree at least 10, there exist non-generated bundles of rank 3 computing one of the Clifford indices.

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