Stably free cancellation for group rings of metacyclic type

John Evans

doi:10.1093/qmath/hay056

Stably free cancellation for group rings of metacyclic type

John Evans

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

Abstract

Let p, q be primes such that q|p−1⁠. Write F_n for the free group of rank n≥1 and let G(p,q)=C_p⋊C_q. We show that any stably free module over Z[G(p,q)×F_n] is necessarily free.

Original language	English
Pages (from-to)	603–618
Number of pages	16
Journal	The Quarterly Journal of Mathematics
Volume	70
Issue number	2
DOIs	https://doi.org/10.1093/qmath/hay056
Publication status	Published - 8 Nov 2018
Externally published	Yes

Keywords

stably free modules
group rings

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10.1093/qmath/hay056

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title = "Stably free cancellation for group rings of metacyclic type",

abstract = "Let p, q be primes such that q|p−1⁠. Write Fn for the free group of rank n≥1 and let G(p,q)=Cp⋊Cq. We show that any stably free module over Z[G(p,q)×Fn] is necessarily free.",

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year = "2018",

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language = "English",

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journal = "The Quarterly Journal of Mathematics",

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N2 - Let p, q be primes such that q|p−1⁠. Write Fn for the free group of rank n≥1 and let G(p,q)=Cp⋊Cq. We show that any stably free module over Z[G(p,q)×Fn] is necessarily free.

AB - Let p, q be primes such that q|p−1⁠. Write Fn for the free group of rank n≥1 and let G(p,q)=Cp⋊Cq. We show that any stably free module over Z[G(p,q)×Fn] is necessarily free.

KW - stably free modules

KW - group rings

U2 - 10.1093/qmath/hay056

DO - 10.1093/qmath/hay056

M3 - Article

SN - 1464-3847

VL - 70

SP - 603

EP - 618

JO - The Quarterly Journal of Mathematics

JF - The Quarterly Journal of Mathematics

IS - 2

ER -

Stably free cancellation for group rings of metacyclic type

Abstract

Keywords

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