scholarly journals A classification of spherical conjugacy classes

2016 ◽  
Vol 285 (1) ◽  
pp. 63-91
Author(s):  
Mauro Costantini
Keyword(s):  
Conjugacy Classes

Classification of Maximal Fuchsian Subsgroups of Some Bianchi Groups

1991 ◽  
Vol 34 (3) ◽  
pp. 417-422 ◽  
Author(s):  
L. Ya. Vulakh
Keyword(s):  
Quadratic Field ◽  
Complete Classification ◽  
Conjugacy Classes ◽  
Imaginary Quadratic Field ◽  
Ring Of Integers

AbstractLet d = 1,2, or p, prime p ≡ 3 (mod 4). Let Od be the ring of integers of an imaginary quadratic field A complete classification of conjugacy classes of maximal non-elementary Fuchsian subgroups of PSL(2, Od) in PGL(2, Od) is given.

Non-discrete Frieze Groups

2016 ◽  
Vol 59 (2) ◽  
pp. 234-243
Author(s):  
Alan F. Beardon
Keyword(s):  
Discrete Subgroup ◽  
Classical Case ◽  
Conjugacy Classes

AbstractThe classification of Euclidean frieze groups into seven conjugacy classes is well known, and many articles on recreational mathematics contain frieze patterns that illustrate these classes. However, it is only possible to draw these patterns because the subgroup of translations that leave the pattern invariant is (by definition) cyclic, and hence discrete. In this paper we classify the conjugacy classes of frieze groups that contain a non-discrete subgroup of translations, and clearly these groups cannot be represented pictorially in any practicalway. In addition, this discussion sheds light onwhy there are only seven conjugacy classes in the classical case.

Classification of finite groups according to the number of conjugacy classes

1985 ◽  
Vol 51 (4) ◽  
pp. 305-338 ◽  
Author(s):  
Antonio Vera López ◽  
Juan Vera López
Keyword(s):  
Finite Groups ◽  
Conjugacy Classes

scholarly journals Complete Classification of Degree 7 for Genus 1

2021 ◽  
pp. 594-603
Author(s):  
Peshawa M. Khudhur
Keyword(s):  
Riemann Surface ◽  
Meromorphic Function ◽  
Symmetric Group ◽  
Compact Riemann Surface ◽  
Complete Classification ◽  
Conjugacy Classes ◽  
Branched Cover ◽  
Transitive Subgroup ◽  
Genus One

Assume that  is a meromorphic fuction of degree n where X is compact Riemann surface of genus g. The meromorphic function gives a branched cover of the compact Riemann surface X. Classes of such covers are in one to one correspondence with conjugacy classes of r-tuples (  of permutations in the symmetric group , in which  and s generate a transitive subgroup G of  This work is a contribution to the classification of all primitive groups of degree 7, where X is of genus one.

scholarly journals On classification of σ-conjugacy classes of a loop group

2016 ◽  
Vol 459 ◽  
pp. 29-42
Author(s):  
Sian Nie ◽  
Peipei Zhou
Keyword(s):  
Loop Group ◽  
Conjugacy Classes

scholarly journals Order 3 Elements in G2 and Idempotents in Symmetric Composition Algebras

2018 ◽  
Vol 70 (5) ◽  
pp. 1038-1075 ◽  
Author(s):  
Alberto Elduque
Keyword(s):  
Conjugacy Classes ◽  
Closed Field ◽  
Algebraically Closed Field ◽  
Exceptional Groups ◽  
Composition Algebras ◽  
Characteristic 3

AbstractOrder three elements in the exceptional groups of type G2 are classiûed up to conjugation over arbitrary fields. Their centralizers are computed, and the associated classification of idempotents in symmetric composition algebras is obtained. Idempotents have played a key role in the study and classification of these algebras.Over an algebraically closed field, there are two conjugacy classes of order three elements in G2 in characteristic not 3 and four of them in characteristic 3. The centralizers in characteristic 3 fail to be smooth for one of these classes.

Conjugacy Classes of Maximal Tori in Simple Real Algebraic Groups and Applications

1994 ◽  
Vol 46 (4) ◽  
pp. 699-717 ◽  
Author(s):  
Dragomir Ž. Doković ◽  
Nguyêñ Quôć Thăńg
Keyword(s):  
Lie Algebras ◽  
Lie Group ◽  
Short Proof ◽  
Algebraic Groups ◽  
Conjugacy Classes ◽  
Exponential Map ◽  
Simple Complex ◽  
Maximal Tori ◽  
Cartan Subalgebras

AbstractLet G be an almost simple complex algebraic group defined over R, and let G(R) be the group of real points of G. We enumerate the G(R)-conjugacy classes of maximal R-tori of G. Each of these conjugacy classes is also a single G(R)˚-conjugacy class, where G(R)˚ is the identity component of G(R), viewed as a real Lie group. As a consequence we also obtain a new and short proof of the Kostant-Sugiura's theorem on conjugacy classes of Cartan subalgebras in simple real Lie algebras.A connected real Lie group P is said to be weakly exponential (w.e.) if the image of its exponential map is dense in P. This concept was introduced in [HM] where also the question of identifying all w.e. almost simple real Lie groups was raised. By using a theorem of A. Borel and our classification of maximal R-tori we answer the above question when P is of the form G(R)˚.

Classifying C1+ structures on dynamical fractals: 2. Embedded trees

1995 ◽  
Vol 15 (5) ◽  
pp. 969-992 ◽  
Author(s):  
A. A. Pinto ◽  
D. A. Rand
Keyword(s):  
Moduli Spaces ◽  
Binary Tree ◽  
Conjugacy Classes ◽  
Expanding Maps ◽  
Bounded Geometry ◽  
Arbitrary Topology ◽  
Contact Points ◽  
Train Tracks ◽  
Smooth Conjugacy

AbstractWe classify the C1+α structures on embedded trees. This extends the results of Sullivan on embeddings of the binary tree to trees with arbitrary topology and to embeddings without bounded geometry and with contact points. We used these results in an earlier paper to describe the moduli spaces of smooth conjugacy classes of expanding maps and Markov maps on train tracks. In later papers we will use those results to do the same for pseudo-Anosov diffeomorphisms of surfaces. These results are also used in the classification of renormalisation limits of C1+α diffeomorphisms of the circle.

Finite Groups with Some Subgroups of Given Order

2013 ◽  
Vol 20 (03) ◽  
pp. 457-462 ◽  
Author(s):  
Jiangtao Shi ◽  
Cui Zhang ◽  
Dengfeng Liang
Keyword(s):  
Finite Groups ◽  
Prime Power ◽  
Solvable Groups ◽  
Complete Classification ◽  
Conjugacy Classes ◽  
Prime Power Order

Let [Formula: see text] be the class of groups of non-prime-power order or the class of groups of prime-power order. In this paper we give a complete classification of finite non-solvable groups with a quite small number of conjugacy classes of [Formula: see text]-subgroups or classes of [Formula: see text]-subgroups of the same order.

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