[PDF] Top 20 On the non–periodic groups, whose subgroups of infinite special rank are transitively normal
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On the non–periodic groups, whose subgroups of infinite special rank are transitively normal
... has infinite special rank, so that K is the least element of ...first infinite ordinal ) includes each members of S which is contained in ...maximal normal abelian subgroup of G. If we ... See full document
11
On groups whose subgroups of infinite special rank are transitively normal
... an infinite elementary abelian p-subgroup V in P ...are infinite subgroups U, W of V , such that V = U × W ...both subgroups hyiU and hyiW have infinite special rank, and, ... See full document
12
Infinite groups with many generalized normal subgroups
... all infinite subgroups of G/T are nearly normal, we have of course that also all infinite subgroups of G are nearly normal; on the other hand, if all infinite ... See full document
11
Groups with many pronormal and transitively normal subgroups
... is non-finitely generated, so that it is transitively ...is normal in P [1, Lemma ...is normal in P . It follows that every subgroup of D is normal in ...The subgroups hgiY and ... See full document
23
Locally soluble groups with the restrictions on the generalized norms
... of infinite order of a group G and all its Abelian non-cyclic ...the periodic part T (C) of the subgroup C is normal in G and C/T (C) is an Abelian torsion-free group of rank ... See full document
14
Structure of Groups with Generalized Normal Subgroups
... all infinite subgroups of G/T are nearly normal, we have of course that also all infinite subgroups of G are nearly normal; on the other hand, if all infinite ... See full document
8
On various rank conditions in infinite groups
... of rank in this general form initially appeared in a paper of ...the special rank has also been called the Pr¨ ufer ...finite special rank turns out to be one of the most important in ... See full document
22
Groups of infinite rank with a normalizer condition on subgroups
... ufer) rank r if every finitely generated subgroup of G can be generated by at most r elements, and r is the least positive integer with such ...its subgroups of infinite rank has been ... See full document
6
Groups with many pronormal and transitively normal subgroups
... index in A. By above remarked, this means that A = A∩C. Moreover, every term of an upper Z(K/A)-central series is a pure G-invariant subgroup. It follows that A = ξ Z(K/A) (A), that is A ≤ ξ(K) and a subgroup K is ... See full document
18
Groups with permutability conditions for subgroups of infinite rank
... every normal subgroup of a group is permutable, but arbitrary permutable subgroups need not to be ...quasihamiltonian groups is well known, we refer to [10] for a detailed ...a ... See full document
10
Groups whose proper subgroups of infinite rank have polycyclic-by-finite conjugacy classes
... proper subgroups of finite index. First assume that all proper normal subgroups of G have finite ...has infinite rank and hence it is not ...finite rank, a contradiction. ... See full document
7
Groups satisfying certain rank conditions
... 4. Groups whose subgroups are (finite rank)-by-soluble Now let R denote the class of groups of finite special ...Finite groups with all subgroups nilpotent were ... See full document
17
On some developments in investigation of groups with prescribed properties of generalized normal subgroups
... finite non-abelian groups whose all subgroups are normal (the Hamiltonian ...Hamiltonian groups together form the (named in honor of Dedekind) class of Dedekind ...all ... See full document
31
On locally finite groups whose cyclic subgroups are \(\mathrm{GNA}\)-subgroups
... an infinite group such that every proper non-identity subgroup is cyclic of prime order p for some fixed ...such groups for any prime number p > 10 75 [13, ...two non-commuting elements ... See full document
12
Generalized norms of groups
... of groups with respect on properties of their Σ-norms is a very important field in the group ...of groups that differ from their Σ-norms as well as groups that have a non-Dedekind Σ-norm ... See full document
34
On soluble groups whose subnormal subgroups are inert
... of whose subgroups are inert is called inertial in [11] where, in the context of gen- eralized soluble groups (with some finiteness conditions), a characterization of inertial groups was ... See full document
8
Finite groups whose minimal subgroups are weakly $\mathcal{H}^{\ast}$-subgroups
... minimal subgroups of G and the cyclic subgroups of order 4 satisfying one of the previously mentioned concepts (recall that a minimal subgroup of G is a subgroup of prime ...order whose minimal ... See full document
11
On Fitting groups whose proper subgroups are solvable
... a normal metabelian nilpotent subgroup of G such that n(G) = nc(B ...every normal abelian subgroup A of G contained in B by the ...for non-central elements and satisfies (∗∗) by the ... See full document
18
Root subgroups of the rank two unitary groups
... elements of the vector spaces are matrices (linear transformations), and our multiplication is as follows: given A and B in , the set of n x n matrices over the field K, let [r] ... See full document
128
On some locally soluble infinite dimensional linear groups
... linear groups of infinite central dimension and infinite p-rank all of whose proper subgroups of infinite p-rank are of finite central ... See full document
10
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