Sectional rank and cohomology

Robert M. Guralnick; Pham Huu Tiep

doi:10.1016/j.jalgebra.2019.04.023

Sectional rank and cohomology

Robert M. Guralnick, Pham Huu Tiep

Mathematics

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

2 Scopus citations

Abstract

Donovan's conjecture implies a bound on the dimensions of cohomology groups in terms of the size of a Sylow p-subgroup and we give a proof of a stronger bound (in terms of sectional p-rank) for dim⁡H¹(G,V). We also prove a reduction theorem for higher cohomology.

Original language	English (US)
Pages (from-to)	434-452
Number of pages	19
Journal	Journal of Algebra
Volume	558
DOIs	https://doi.org/10.1016/j.jalgebra.2019.04.023
State	Published - Sep 15 2020

Keywords

Group cohomology
Sectional rank

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/j.jalgebra.2019.04.023

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abstract = "Donovan's conjecture implies a bound on the dimensions of cohomology groups in terms of the size of a Sylow p-subgroup and we give a proof of a stronger bound (in terms of sectional p-rank) for dim⁡H1(G,V). We also prove a reduction theorem for higher cohomology.",

keywords = "Group cohomology, Sectional rank",

author = "Guralnick, {Robert M.} and Tiep, {Pham Huu}",

note = "Funding Information: The first author was partially supported by the NSF grant DMS-1600056. The second author was partially supported by the NSF grant DMS-1840702. The paper is partially based upon work supported by the NSF under grant DMS-1440140 while both authors were in residence at the Mathematical Sciences Research Institute in Berkeley, California, during the Spring 2018 semester. It is a pleasure to thank the Institute for support, hospitality, and stimulating environment. Funding Information: The first author was partially supported by the NSF grant DMS-1600056. The second author was partially supported by the NSF grant DMS-1840702. The paper is partially based upon work supported by the NSF under grant DMS-1440140 while both authors were in residence at the Mathematical Sciences Research Institute in Berkeley, California, during the Spring 2018 semester. It is a pleasure to thank the Institute for support, hospitality, and stimulating environment.☆ The first author was partially supported by the NSF grant DMS-1600056. The second author was partially supported by the NSF grant DMS-1840702. The paper is partially based upon work supported by the NSF under grant DMS-1440140 while both authors were in residence at the Mathematical Sciences Research Institute in Berkeley, California, during the Spring 2018 semester. It is a pleasure to thank the Institute for support, hospitality, and stimulating environment. Publisher Copyright: {\textcopyright} 2019 Elsevier Inc.",

year = "2020",

month = sep,

day = "15",

doi = "10.1016/j.jalgebra.2019.04.023",

language = "English (US)",

volume = "558",

pages = "434--452",

journal = "Journal of Algebra",

issn = "0021-8693",

publisher = "Academic Press Inc.",

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T1 - Sectional rank and cohomology

AU - Guralnick, Robert M.

AU - Tiep, Pham Huu

N1 - Funding Information: The first author was partially supported by the NSF grant DMS-1600056. The second author was partially supported by the NSF grant DMS-1840702. The paper is partially based upon work supported by the NSF under grant DMS-1440140 while both authors were in residence at the Mathematical Sciences Research Institute in Berkeley, California, during the Spring 2018 semester. It is a pleasure to thank the Institute for support, hospitality, and stimulating environment. Funding Information: The first author was partially supported by the NSF grant DMS-1600056. The second author was partially supported by the NSF grant DMS-1840702. The paper is partially based upon work supported by the NSF under grant DMS-1440140 while both authors were in residence at the Mathematical Sciences Research Institute in Berkeley, California, during the Spring 2018 semester. It is a pleasure to thank the Institute for support, hospitality, and stimulating environment.☆ The first author was partially supported by the NSF grant DMS-1600056. The second author was partially supported by the NSF grant DMS-1840702. The paper is partially based upon work supported by the NSF under grant DMS-1440140 while both authors were in residence at the Mathematical Sciences Research Institute in Berkeley, California, during the Spring 2018 semester. It is a pleasure to thank the Institute for support, hospitality, and stimulating environment. Publisher Copyright: © 2019 Elsevier Inc.

PY - 2020/9/15

Y1 - 2020/9/15

N2 - Donovan's conjecture implies a bound on the dimensions of cohomology groups in terms of the size of a Sylow p-subgroup and we give a proof of a stronger bound (in terms of sectional p-rank) for dim⁡H1(G,V). We also prove a reduction theorem for higher cohomology.

AB - Donovan's conjecture implies a bound on the dimensions of cohomology groups in terms of the size of a Sylow p-subgroup and we give a proof of a stronger bound (in terms of sectional p-rank) for dim⁡H1(G,V). We also prove a reduction theorem for higher cohomology.

KW - Group cohomology

KW - Sectional rank

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U2 - 10.1016/j.jalgebra.2019.04.023

DO - 10.1016/j.jalgebra.2019.04.023

M3 - Article

SN - 0021-8693

VL - 558

SP - 434

EP - 452

JO - Journal of Algebra

JF - Journal of Algebra

ER -

Sectional rank and cohomology

Abstract

Keywords

ASJC Scopus subject areas

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