[PDF] Top 20 Commutator Length of Finitely Generated Linear Groups
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Commutator Length of Finitely Generated Linear Groups
... the commutator length of a free nilpotent group of rank n is at most ...nilpotent groups of rank n by Allambergenov and Roman’kov ...the commutator length of elements of free ... See full document
5
On Solvable Groups of Arbitrary Derived Length and Small Commutator Length
... the commutator length of this class of ...solvability length of the group, and the number of generators of the group G k as a ...a finitely generated solvable group G, each term of the ... See full document
6
Groups with minimax commutator subgroup
... every finitely generated subgroup of G can be generated by at most r elements, and r is the least positive integer with such ...the commutator subgroup G 0 of G is ...the commutator ... See full document
8
On invertor elements and finitely generated subgroups of groups acting on trees with inversions
... finitely generated subgroup H of G a conjugate of H contains a cyclically reduced ele- ment of length at least one or H is contained in a conjugate of a factor of ... See full document
11
Metahamiltonian groups and related topics
... every finitely generated subgroup of G can be generated by at most r elements, and r is the smallest positive integer with such ...of groups whose proper subgroups of infinite rank belong to a ... See full document
13
On the commutator lengths of certain classes of finitely presented groups
... finite groups for their maximal lengths and find upper bounds for the commutator ...The groups studied here are the dihedral groups D 2n = a,b | a 2 = b n = (ab) 2 = 1 , n ≥ 3, the quaternion ... See full document
9
On the commutator lengths of certain classes of finitely presented groups
... This notion has been studied by many authors during the years and the results of the combinatorial methods estimate or calculate the commutator lengths of abstract groups which are mainly infinite (one may ... See full document
10
On Semiabelian Groups
... abelian finitely generated group. Since G is two-generated nonpe- riodic, D is at most two-generated, and D = ...of groups G i , i ∈ I, if it satisfies the following ... See full document
6
Rationality of blocks of quasi-simple finite groups
... Proof. Let ˆ G denote a finite group such that G C G ˆ and ˆ G/Z( ˆ G) is a symmetric group, and let ˆ b denote a block of O G ˆ covering b. Since we may assume that b and hence ˆ b does not have cyclic defect ... See full document
24
Periodic rings with finitely generated underlying group
... We study periodic rings that are finitely generated as groups. We prove several structure results. We classify periodic rings that are free of rank at most 2, and also periodic rings R such that R is finitely ... See full document
6
Ore's theorem
... structure of finite abelian groups and finitely generated abelian groups, Ore's Theorem and its corollaries provide us with several results relating distributive lattices with cyclic g[r] ... See full document
44
MoL 2001 09: Finite Projective Formulas
... Suppose a frame (W, R) is given. Let x < y mean xRy and x 6= y. For w, v ∈ W , v is said to cover w, if w < v and there does not exist u such that w < u < v. A ⊆ W is called an anti-chain of W , if for all w, ... See full document
49
On the Homomorphisms of n D Behaviors
... The central result of Oberst in [8, 2.54], is that the signal spaces identified are injective cogenerators. One restatement of this result is that is a faithfully exact con- travariant functor, and therefore we have a ... See full document
11
Twisted conjugacy and quasi isometric rigidity of irreducible lattices in semisimple lie groups
... A lattice Λ in G is said to be irreducible if, for any non-compact closed normal subgroup H of G, the image of Λ under the quotient G → G/H is dense. This definition of irreducibility differs from the definition used in ... See full document
10
Finitely Generated Annihilating-Ideal Graph of Commutative Rings
... In [2], the authors studied rings for which annihilating-ideal graph is bipartite and star graph, the following two proposition shows that finitely generated annihilating-ideal graph is bi- partite (star) ... See full document
9
Generators and relations for subsemigroups via boundaries in Cayley graphs
... δ ∈ B ∗ , and A ∩ B = ∅. In contrast, it is easy to see that the free commutative semigroup h a, b | ab = ba i does not have splitting parallel paths (nor would we expect it to, since its Cayley graph is not at all ... See full document
36
Projectivity and flatness over the endomorphism ring of a finitely generated module
... In fact, both results are special cases of a more general result which happens to be very elementary. Let Λ be a finitely generated module over a ring A, and B the endomorphism ring of Λ . Adapting the techniques ... See full document
8
Cryptographic Protocols Based on Nielsen Transformations
... a linear technique to study free groups and general infinite ...is generated by a regular Nielsen transformation between two basis of F , and each regular Nielsen transformation between two bases of ... See full document
46
Computing invariants for finitely presented nilpotent groups
... The second problem centres on classifying finitely generated, torsion- free nilpotent groups of class 2 . Canonical presentations can be given for each such group. A skew-symmetric matrix can be ... See full document
178
Restrictions on commutativity ratios in finite groups
... We call Pr(G) the commutativity ratio of G, but others sometimes refer to it as the ‘commutativity degree’ of the group G; this phrase has another well-established meaning in the theory of p-groups and so we will ... See full document
12
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