Certain homological functors of 2-generator 𝑝-groups of class 2

Magidin, Arturo; Morse, Robert Fitzgerald

doi:10.1090/conm/511/10046

Cited by 17 publications

(17 citation statements)

References 14 publications

(37 reference statements)

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…E 1 is the extraspecial group of order p 3 and odd prime exponent p; G p .˛;ˇ; I ; / is the 2-generator p-group of class 2 introduced in [16] with the following presentation:…”

Section: S Hadi Jafari and H Hadizadehmentioning

confidence: 99%

On the triple tensor product of prime-power groups

Jafari

Hadizadeh

2020

Journal of Group Theory

View full text Add to dashboard Cite

Let G be a finite p-group, and let {\otimes^{3}G} be its triple tensor product. In this paper, we obtain an upper bound for the order of {\otimes^{3}G}, which sharpens the bound given by G. Ellis and A. McDermott, [Tensor products of prime-power groups, J. Pure Appl. Algebra 132 1998, 2, 119–128]. In particular, when G has a derived subgroup of order at most p, we classify those groups G for which the bound is attained. Furthermore, by improvement of a result about the exponent of {\otimes^{3}G} determined by G. Ellis [On the relation between upper central quotients and lower central series of a group, Trans. Amer. Math. Soc. 353 2001, 10, 4219–4234], we show that, when G is a nilpotent group of class at most 4, {\exp(\otimes^{3}G)} divides {\exp(G)}.

show abstract

“…E 1 is the extraspecial group of order p 3 and odd prime exponent p; G p .˛;ˇ; I ; / is the 2-generator p-group of class 2 introduced in [16] with the following presentation:…”

Section: S Hadi Jafari and H Hadizadehmentioning

confidence: 99%

On the triple tensor product of prime-power groups

Jafari

Hadizadeh

2020

Journal of Group Theory

View full text Add to dashboard Cite

show abstract

“…A complete classification of 2-generated finite capable p-groups of class 2 is given in [15]. Motivated by finite extraspecial p-groups, a more general class of groups G admitting Property A can be constructed as follows.…”

Section: And Equality Holds If G Is Nilpotent Somentioning

confidence: 99%

Central Quotient Versus Commutator Subgroup of Groups

Yadav

2016

Springer Proceedings in Mathematics &Amp; Statistics

View full text Add to dashboard Cite

“…Based on this new classification, Magidin and Morse give a complete determination of all capable two-generator p-groups of class 2, using a unified approach and modified tensor methods [14]. Thus with the exception of the non-torsion groups among them, the question of capability for two-generator groups of class 2 has been settled, since it suffices to consider the Sylow p-subgroups in case of finite two-generator groups of nilpotency class 2.…”

Section: Definition 15 ([7]) For Any Group G the Exterior Square Omentioning

confidence: 99%

On the Capability of Finitely Generated Non-Torsion Groups of Nilpotency Class 2

Kappe

Ali²,

Sarmin³

2011

Glasgow Math. J.

View full text Add to dashboard Cite

Abstract.A group is called capable if it is a central factor group. In this paper, we establish a necessary condition for a finitely generated non-torsion group of nilpotency class 2 to be capable. Using the classification of two-generator non-torsion groups of nilpotency class 2, we determine which of them are capable and which are not and give a necessary and sufficient condition for a two-generator non-torsion group of class 2 to be capable in terms of the torsion-free rank of its factor commutator group.2010 Mathematics Subject Classification. 20D15, 20J05.

show abstract

Certain homological functors of 2-generator 𝑝-groups of class 2

Cited by 17 publications

References 14 publications

On the triple tensor product of prime-power groups

On the triple tensor product of prime-power groups

Central Quotient Versus Commutator Subgroup of Groups

On the Capability of Finitely Generated Non-Torsion Groups of Nilpotency Class 2

Contact Info

Product

Resources

About