On a construction related to the non-abelian tensor square of a group

Rocco, Noraí R.

doi:10.1007/bf01244898

Cited by 76 publications

(119 citation statements)

References 8 publications

Supporting

Mentioning

110

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%

“…Definition 3 [7,9]. Let G be a group with presentation R G and let G be an isomorphic copy of G via the mapping : g g for all g G .…”

Section: Preliminary Resultsmentioning

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

“…Rocco [15] and later Ellis [5] showed that where exp(G ab ) = p e is the exponent of G ab (e is a positive integer). If G ab is an elementary abelian p-group, then one can see that (1.4), (1.5), and (1.6) are all equal.…”

Section: Introduction and Statement Of Resultsmentioning

confidence: 99%

On the size of the third homotopy group of the suspension of an Eilenberg--MacLane space

Niroomand¹,

Russo²

2014

Turk J Math

View full text Add to dashboard Cite

The nonabelian tensor square G ⊗ G of a group G of |G| = p n and |G ′ | = p m ( p prime and n, m ≥ 1 ) satisfies a classic bound of the form |G ⊗ G| ≤ p n (n−m) . This allows us to give an upper bound for the order of the third homotopy group π3(SK(G, 1)) of the suspension of an Eilenberg-MacLane space K(G, 1) , because π3(K(G, 1)) is isomorphic to the kernel of κ : −m) but also supporting a recent result of Jafari on the topic. Consequently, we discuss restrictions on the size of π3(SK(G, 1)) based on this new estimation.

show abstract

“…Details can be found in [9,12,15]. If one looks at G and H as normal subgroups of a bigger group M , then the following argument may be applied (see for instance [9, p. 23]).…”

Section: Resultsmentioning

confidence: 99%

“…Brown and others wrote two fundamental contributions [4,5] on the so-called nonabelian tensor square of a group, leaving a series of open questions which have been successively discussed in [6,7,9,10,11,12,15,16,19,20] and in other works of different authors in recent years.…”

Section: Formulation Of the Problem In Terms Of Class Operatorsmentioning

confidence: 99%