[PDF] Top 20 Camina groups with few conjugacy classes
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Camina groups with few conjugacy classes
... a Camina group, unless K = 1, and in such a case the group G is ...abelian. Camina groups were introduced by A.R. Camina in [1], and they have been extensively studied by Macdonald, Chillag, ... See full document
10
Conjugacy and order classes of two-generator p-groups of nilpotency class two
... Trebenko [7] attempted a classification of all 2-generator groups of class 2. In 1993, Bacon and Kappe [8] complete and correct Trebenko’s paper to produce a classification of 2-generator p-groups of class ... See full document
16
The exact number of conjugacy classes for 2 - generator p - groups of nilpotency class 2
... Chapter 5 provides GAP programmes that have been used to construct examples for 2-generator p-groups of class 2 (p an odd prime). Not only that, the properties of these groups can be computed and lead to ... See full document
17
On the Conjugacy Classes, Centers and Representation of the Groups Sn and Dn and the subgroups of the Dihedral group Dn.
... The group structures of Sn and Dn were examined and their Conjugacy classes. It was found that all conjugate elements in Sn have the same cycle type, i.e. if α,σ∈ Sn such that α is conjugate to σ, then l(α) ... See full document
8
Non-nilpotent groups with three conjugacy classes of non-normal subgroups
... In the groups (vii),..., (x), N is normal of order q ( in the group (vii), (viii) and (x), N = G 0 and in the group (ix), N is characteristic in G 0 ); so H 6 P. For the group (x), H is a maximal or second maximal ... See full document
7
A note on maximal length elements in conjugacy classes of finite coxeter groups
... of conjugacy classes of involutions, a rule to determine the minimal and maximal length in the class is given in [10], and a complete description of the set of elements of maximal and minimal length appears ... See full document
10
Groups whose proper subgroups of infinite rank have polycyclic-by-finite conjugacy classes
... Proof. In view of Lemma 2.4, one can assume that G/G ′ has finite rank, so G ′ has infinite rank. First consider the case when G/G ′ is finitely generated. Then G has a maximal subgroup, say M , containing G ′ . So M is ... See full document
7
Conjugacy classes contained in normal subgroups: an overview
... the conjugacy classes contained in a normal subgroup and their sizes exert an influence on the normal structure of a finite ...the conjugacy classes, which have been introduced and developed ... See full document
14
On Some Problems in Group Theory of Probabilistic Nature
... The Groups, Algorithms & Programming (GAP) Software is used to identify the groups that fulfill the classification and to confirm the number of conjugacy classes of a ...the groups ... See full document
7
Conjugacy in relatively extra-large Artin groups
... (*) If a word in level i is shorter than its immediate predecessor, then erase all its predecessors. The different words in each tree (connected component) form an equivalence class, which is the orbit under ⟨K , L⟩ on ... See full document
41
Character expansiveness in finite groups
... than conjugacy expansiveness. We say that G is normal conjugacy expansive if for any normal subgroup N and any conjugacy class C of G the normal set N C consists of at least as many conjugacy ... See full document
9
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
Groups with reality and conjugacy conditions
... finite groups with this property are ...such groups have been obtained by Camina ([3]) and Dolfi and Jabara ...non-trivial conjugacy class ... See full document
14
On the number of the irreducible characters of factor groups
... for conjugacy classes of ...the conjugacy classes of G, contained in the normal subgroup N and classified finite solvable groups G in which the set K(G) = {ξ(N )|N E G, N 6= G} contains ... See full document
6
Transformation Semigroups Over Groups
... The following theorem, which gives a formula for de- termining the number of conjugacy classes in GwrT n , is analogous to the formula for the number of conjugacy classes in GwrS n.. So,[r] ... See full document
99
Countably recognizable classes of groups with restricted conjugacy classes
... free groups is not countably ...cyclic groups cannot be decomposed into a direct product of infinite cyclic groups, but all its countable subgroups are free abelian (see for instance [6, Theorem ... See full document
12
On finite groups with square-free conjugacy class sizes
... finite groups will be considered in this expository ...of conjugacy class sizes on the structure of finite groups has been thoroughly ...of Camina and Camina ...the conjugacy ... See full document
8
Conjugacy classes and graphs of two-groups of nilpotency class two
... the conjugacy classes on the structure of a finite group have been the subject of research over the ...the conjugacy class sizes depend on the order of the commutator ... See full document
24
Some problems about products of conjugacy classes in finite groups
... Some results of this survey were obtained during the stay of C. Melchor at the University of Cam- bridge in autumn 2017, which was financially supported by the grant E-2017-02, Universitat Jaume I of Castell´ on. She ... See full document
10
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
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