Computing the nonabelian tensor squares of polycyclic groups

Blyth, Russell D.; Morse, Robert Fitzgerald

doi:10.1016/j.jalgebra.2008.12.029

Cited by 42 publications

(40 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…The structural results of ) (G , which is polycyclic, was studied by Ellis and Leonard [7], Rocco [9] and has been extended by Blyth and Morse [10], and is given as follows.…”

Section: Preliminary Resultsmentioning

confidence: 99%

See 1 more Smart Citation

The nonabelian tensor square of Bieberbach group of dimension five with dihedral point group of order eight

Fauzi

Idrus

Masri

et al. 2014

AIP Conference Proceedings

View full text Add to dashboard Cite

“…The structural results of ) (G , which is polycyclic, was studied by Ellis and Leonard [7], Rocco [9] and has been extended by Blyth and Morse [10], and is given as follows.…”

Section: Preliminary Resultsmentioning

confidence: 99%

“…(ii) In order to determine the structure of G G , we compute ) (G using the following proposition that had been proved in [10].…”

Section: Theorem 1 [9]mentioning

confidence: 99%

The nonabelian tensor square of Bieberbach group of dimension five with dihedral point group of order eight

Fauzi

Idrus

Masri

et al. 2014

AIP Conference Proceedings

View full text Add to dashboard Cite

“…It was shown in [1] that if H is polycyclic then so is ν(H). Thus, the following corollary generalizes this result.…”

Section: Then the Schur Multiplier M (H) Is Isomorphic The Quotient Jmentioning

confidence: 99%

Weak commutativity between two isomorphic polycyclic groups

Lima

Oliveira

2016

Journal of Group Theory

View full text Add to dashboard Cite

Abstract. The operator of weak commutativity between isomorphic groups H and H ψ was defined by Sidki asIt is known that the operator χ preserves group properties such as finiteness, solubility and also nilpotency for finitely generated groups. We prove in this work that χ preserves the properties of being polycyclic and polycyclic by finite. As a consequence of this result, we conclude that the non-abelian tensor square H ⊗ H of a group H, defined by Brown and Loday, preserves the property polycyclic by finite. This last result extends that of Blyth and Morse who proved that H ⊗ H is polycyclic if H is polycyclic.

show abstract

“…(1) The method developed by Blyth and Morse [7], which is aided by the following proposition, is used to compute the central subgroup of its nonabelian tensor square. Proposition 2 [7].…”

Section: Introductionmentioning

confidence: 99%

“…Proposition 2 [7]. Let G be a polycyclic group with a polycyclic generating sequence 1 ,......, k g g .…”

Section: Introductionmentioning

confidence: 99%

The central subgroup of the nonabelian tensor square of a torsion free space group

Mohammad

Sarmin²,

Hassim³

2016

AIP Conference Proceedings

View full text Add to dashboard Cite

Abstract. Space groups of a crystal expound its symmetry properties. One of the symmetry properties is the central subgroup of the nonabelian tensor square of a group. It is a normal subgroup of the group which can be ascertained by finding the abelianisation of the group and the nonabelian tensor square of the abelianisation group. In this research, our focus is to explicate the central subgroup of the nonabelian tensor square of the torsion free space groups of a crystal which are called the Bieberbach groups.

show abstract

Computing the nonabelian tensor squares of polycyclic groups

Cited by 42 publications

References 22 publications

The nonabelian tensor square of Bieberbach group of dimension five with dihedral point group of order eight

The nonabelian tensor square of Bieberbach group of dimension five with dihedral point group of order eight

Weak commutativity between two isomorphic polycyclic groups

The central subgroup of the nonabelian tensor square of a torsion free space group

Contact Info

Product

Resources

About