[PDF] Top 20 Some problems about products of conjugacy classes in finite groups
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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. ... See full document
10
Countably recognizable classes of groups with restricted conjugacy classes
... of groups with finite conjugacy classes is to establish conditions under which a periodic residually finite F C -group can be embedded into the direct product of a collection of ... See full document
12
Generation problems for finite groups
... with r ∈ F G. If V is any F G-module possessing two submodules M and N such that V = M + N and M ∩ N = 0, then V ∼ = M ⊕ N (defined as above). We call this situation the internal direct sum and note that due to this ... See full document
110
Groups whose proper subgroups of infinite rank have polycyclic-by-finite conjugacy classes
... has finite rank, a ...has finite rank, then it is almost locally soluble [5] and hence locally soluble as G has no proper subgroups of finite ...of finite rank, then HN is a proper subgroup of ... See full document
7
Conjugacy classes and graphs of two-groups of nilpotency class two
... of conjugacy classes have sparked many interests among researchers in group theory over the past ...of conjugacy classes for finite groups has already been considered by many ... See full document
24
The commutativity degree of some nonabelian two-groups with a cyclic subgroup of index four
... a finite group has been introduced for symmetric groups, finite groups and finite rings in the last fifty ...of some nonabelian 2-groups with a cyclic subgroup of index ... See full document
19
Some numerical results on two classes of finite groups
... Polkouei, Some numerical results on finite non-abelian 2- generator p-groups of nilpotency class two , Annals Math Iasi, preprinted.. Sarmin, On some problems in group theory of probabil[r] ... See full document
10
Finite groups with the same conjugacy class sizes as a finite simple group
... Definition 2.9. [17] For a group H, the number of isomorphism classes of groups with the same set OC(H) of order components is denoted by h(OC(H)). If h(OC(H)) = k, then H is called k-recognizable by the ... See full document
11
Character expansiveness in finite groups
... a finite group G 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 ... See full document
9
Orbit counting in conjugacy classes for free groups acting on trees
... both finite and infinite reduced words which will encode the lengths L(x) and which will also give the lengths of closed geodesics by summing the function around the corresponding periodic ...results about ... See full document
14
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
Non-nilpotent groups with three conjugacy classes of non-normal subgroups
... a finite group. We denote by ν(G) the number of conjugacy classes of non-normal subgroups of ...classified finite groups with ν(G) = ...of finite groups, so many authors ... See full document
7
The Multiplicative Degree of Some Finite Groups
... the finite groups, G are ...of conjugacy classes in order to determine the commutativity degree of finite p-groups of nilpotency class ...the conjugacy class was first ... See full document
6
Conjugacy and order classes of two-generator p-groups of nilpotency class two
... a finite group and x, y ∈ ...The conjugacy class containing the identity has only an element namely the ...own conjugacy class containing only that ... See full document
16
On the Conjugacy Classes, Centers and Representation of the Groups Sn and Dn and the subgroups of the Dihedral group Dn.
... Permutation groups and matrix groups are special cases of transformation groups; group that act on a certain space X preserving its inherent ...permutation groups, X is a ...any finite ... See full document
8
The exact number of conjugacy classes for 2 - generator p - groups of nilpotency class 2
... nilpotent groups that have been classified. In this research, 2-generator p- groups of nilpotency class 2 (p an odd prime) are ...These groups were classified by Bacon and Kappe in 1993 and Kappe, ... See full document
17
A note on maximal length elements in conjugacy classes of finite coxeter groups
... gacy classes of Weyl ...the conjugacy classes of finite Coxeter groups, and prin- cipally those of the irreducible finite Coxeter groups, has come from many directions, ... See full document
10
On finite groups with square-free conjugacy class sizes
... In general, the product of two supersoluble normal subgroups of a finite group needs not to be supersoluble. This fact originated the inquire of new permutability conditions (stronger than the normality of the ... See full document
8
Statistics in conjugacy classes in free groups
... of finite type. This subshift of finite type is formed from the space of infinite reduced words (with the obvious definition) adjoined to the elements of together with the dynamics given by the action of ... See full document
15
Asymptotics in conjugacy classes for free groups
... counting problems studied by Huber, including the prime geodesic ...counting problems in this collection concern groups of isometries acting on the hyperbolic ... See full document
105
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