@article{40dcf63af6a94d81804dc0214ff4cb93,

title = "Sectional rank and cohomology",

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 dimH1(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.",

}