[PDF] Top 20 Statistics in conjugacy classes in free groups
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Statistics in conjugacy classes in free groups
... follows from Proposition 8 of [14]. The results in [14] are proved for co-compact groups of isometries of real hyperbolic space but go over to co-compact groups of isometries of CAT(−1) spaces by the ... See full document
15
Orbit counting in conjugacy classes for free groups acting on trees
... Remark 2.2. Another subshift of finite type naturally associated to the graph is obtained by taking infinite paths, i.e. infinite sequences of oriented edges with the restriction that e 0 can follow e only if e ... See full document
14
Asymptotics in conjugacy classes for free groups
... In analogy to Huber’s third problem, we consider the orbit counting problem in conjugacy classes in the setting of metric graphs. Rather than compact hyperbolic surfaces with constant negative curvature −1, ... See full document
105
Countably recognizable classes of groups with restricted conjugacy classes
... are free. Therefore the class of free groups is not countably ...being free abelian cannot be detected from the behaviour of countable subgroups; in fact, the cartesian product of any infinite ... See full document
12
On finite groups with square-free conjugacy class sizes
... The previous development was enhanced, firstly by Li, and later on by Liu, Wang and Wei, by replacing conditions for all conjugacy classes by those referring only to a smaller set of elements in G: Theorem ... See full document
8
Modular Subgroups, Dessins d’Enfants and Elliptic K3 Surfaces
... 33 conjugacy classes of congruence, torsion-free, genus zero subgroups of the modular group, especially their j- invariants, dessins and Schreier coset ...some conjugacy class of index 24 ... See full document
44
Conjugacy and subgroups of word hyperbolic groups
... In Section 4.3 it was pointed out that at least some of these facts are not true for general graphs, but it may be that they generalise to more specific classes, like regular graphs (ie. those graphs in which ... See full document
133
Character expansiveness in finite groups
... is conjugacy expansive if for any normal subset S and any conjugacy class C of G the normal set SC consists of at least as many conjugacy classes of G as S ...is conjugacy expansive if ... See full document
9
Conjugacy classes contained in normal subgroups: an overview
... be noted that similar results have also been studied for other graphs. In [19], S. Dolfi defines the dual graph of Γ(G) whose vertices are the primes which occur as divisors of the class sizes of G, and two vertices p ... See full document
14
Groups with reality and conjugacy conditions
... the groups G in which all non-trivial real elements are ...finite groups. We extend this result to periodic F C -groups (Theorem ...finite groups G in which ”all non-trivial real elements are ... See full document
14
Finite non-nilpotent groups with few non-normal non-cyclic subgroups
... Chen , Finite nilpotent groups having exactly four conjugacy classes of non-normal subgroups, Algebra Colloq. Meng , On solvability of finite groups with few non-normal subgroups, Comm[r] ... See full document
6
On the number of the irreducible characters of factor groups
... Example 3.2. Consider the group G = SmallGroup(20, 1), the first group of order 20 in the library of GAP [2]. Then, it is easy to see that G is case (iv) in Theorem A. Therefore, C(G) = {1, 2, 4}. However, we may check ... See full document
6
Conjugacy in relatively extra-large Artin groups
... Now let A be a relatively extra-large Artin group and let M be an annular R -diagram with connected interior. When forming M ′ from M then in contrast to the simply connected case it may happen that ∆(D) is not ... See full document
41
On Some Problems in Group Theory of Probabilistic Nature
... Note that the extra condition a + b 2 3 is added in (2.1.2) to avoid that the Dihedral group of order 8 is not included in both (2.1.1) and (2.1.2). Instead, it is characterized to be of type (2.1.1). The condition a + b ... See full document
7
Toric Heaps, Cyclic Reducibility, and Conjugacy in Coxeter Groups
... DOI: 10.4236/ojdm.2019.94010 115 Open Journal of Discrete Mathematics ative (TFC) and faux CFC . The former are the elements that have only one cyclic commutativity class, and the latter are those that additionally admit ... See full document
34
Conjugacy in braid groups and the LKB representation : and Bessis Garside groups of rank 3
... the conjugacy problem in braid groups, mainly focussing on a sequence of papers by Birman, Gebhardt, and Gonzales-Meneses, [10][11][12], in which they present a scheme for solving the conjugacy ... See full document
94
Maximal tori in finite groups of lie type
... between the conjugacy classes of maximal tori in the finite group and certain equivalence classes in the corresponding Weyl group... result, and its consequences, is discussed in Chapter[r] ... See full document
175
Conjugacy Separability of Some One Relator Groups
... It is obvious that group A is the ordinary free product of the cyclic group X of order m, generated by element a, and the infinite cycle Y , generated by d. The canonical homomorphism of group A onto group A maps ... See full document
14
The exact number of conjugacy classes for 2 - generator p - groups of nilpotency class 2
... In Chapter 2, the bounds on the number of conjugacy classes for nilpotent groups given by several researchers are compared. We show that the bounds exist are very weak. The original classification of ... See full document
17
The conjugacy classes of metabelian groups of order at most 24
... A conjugacy class is an equivalence relation; therefore it partitions the group into disjoint equivalence classes or ...the classes together with those at the centre as well as the identity must ... See full document
5
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