Tensor products of prime-power groups

Graham Ellis; Aidan McDermott

doi:10.1016/S0022-4049(97)00112-6

Tensor products of prime-power groups

Graham Ellis
, Aidan McDermott

Research output: Contribution to journal › Article › peer-review

17 Scopus citations

Abstract

We give a bound for the order of the nonabelian tensor product of two prime-power groups. From this we obtain bounds on the third homotopy group of a union of two spaces. We illustrate our bound by using a GAP computer program to determine the order of the nonabelian tensor product G ⊗ H for all normal subgroups G and H of the quaternion group of order 32.

Original language	English (US)
Pages (from-to)	119-128
Number of pages	10
Journal	Journal of Pure and Applied Algebra
Volume	132
Issue number	2
DOIs	https://doi.org/10.1016/S0022-4049(97)00112-6
State	Published - Nov 10 1998
Externally published	Yes

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/S0022-4049(97)00112-6

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abstract = "We give a bound for the order of the nonabelian tensor product of two prime-power groups. From this we obtain bounds on the third homotopy group of a union of two spaces. We illustrate our bound by using a GAP computer program to determine the order of the nonabelian tensor product G ⊗ H for all normal subgroups G and H of the quaternion group of order 32.",

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Y1 - 1998/11/10

N2 - We give a bound for the order of the nonabelian tensor product of two prime-power groups. From this we obtain bounds on the third homotopy group of a union of two spaces. We illustrate our bound by using a GAP computer program to determine the order of the nonabelian tensor product G ⊗ H for all normal subgroups G and H of the quaternion group of order 32.

AB - We give a bound for the order of the nonabelian tensor product of two prime-power groups. From this we obtain bounds on the third homotopy group of a union of two spaces. We illustrate our bound by using a GAP computer program to determine the order of the nonabelian tensor product G ⊗ H for all normal subgroups G and H of the quaternion group of order 32.

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UR - https://www.scopus.com/pages/publications/0032505950#tab=citedBy

U2 - 10.1016/S0022-4049(97)00112-6

DO - 10.1016/S0022-4049(97)00112-6

M3 - Article

AN - SCOPUS:0032505950

SN - 0022-4049

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SP - 119

EP - 128

JO - Journal of Pure and Applied Algebra

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Tensor products of prime-power groups

Abstract

ASJC Scopus subject areas

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