Suzuki–Ree groups and Tits mixed groups over rings

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Suzuki–Ree groups and Tits mixed groups over rings. / Smolensky, Andrei.

In: Communications in Algebra, Vol. 48, No. 2, 01.02.2020, p. 815-825.

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

Author

Smolensky, Andrei. / Suzuki–Ree groups and Tits mixed groups over rings. In: Communications in Algebra. 2020 ; Vol. 48, No. 2. pp. 815-825.

BibTeX

@article{280d081cd4ff466a9ef7b7d2d2d5447d,

title = "Suzuki–Ree groups and Tits mixed groups over rings",

abstract = "It is shown that Suzuki–Ree groups can be easily defined by means of comparing two fundamental representations of the ambient Chevalley group in characteristic 2 or 3. This eliminates the distinction between the Suzuki–Ree groups over perfect and imperfect fields and gives a natural definition for the analogs of such groups over commutative rings. As an application of the same idea, we explicitly construct a pair of polynomial maps between the groups of types (Formula presented.) and (Formula presented.) in characteristic 2 that compose to the Frobenius endomorphism. This, in turn, provides a simple definition for the Tits mixed groups over rings.",

keywords = "Suzuki—Ree groups, Tits mixed groups, Suzuki-Ree groups, SUBGROUPS",

author = "Andrei Smolensky",

note = "Funding Information: The research was supported by Russian Science Foundation (RSF) (project No. 17-11-01261). Publisher Copyright: {\textcopyright} 2019, {\textcopyright} 2019 Taylor & Francis Group, LLC. Copyright: Copyright 2019 Elsevier B.V., All rights reserved.",

year = "2020",

month = feb,

day = "1",

doi = "10.1080/00927872.2019.1662913",

language = "English",

volume = "48",

pages = "815--825",

journal = "Communications in Algebra",

issn = "0092-7872",

publisher = "Taylor & Francis",

number = "2",

}

RIS

TY - JOUR

T1 - Suzuki–Ree groups and Tits mixed groups over rings

AU - Smolensky, Andrei

N1 - Funding Information: The research was supported by Russian Science Foundation (RSF) (project No. 17-11-01261). Publisher Copyright: © 2019, © 2019 Taylor & Francis Group, LLC. Copyright: Copyright 2019 Elsevier B.V., All rights reserved.

PY - 2020/2/1

Y1 - 2020/2/1

N2 - It is shown that Suzuki–Ree groups can be easily defined by means of comparing two fundamental representations of the ambient Chevalley group in characteristic 2 or 3. This eliminates the distinction between the Suzuki–Ree groups over perfect and imperfect fields and gives a natural definition for the analogs of such groups over commutative rings. As an application of the same idea, we explicitly construct a pair of polynomial maps between the groups of types (Formula presented.) and (Formula presented.) in characteristic 2 that compose to the Frobenius endomorphism. This, in turn, provides a simple definition for the Tits mixed groups over rings.

AB - It is shown that Suzuki–Ree groups can be easily defined by means of comparing two fundamental representations of the ambient Chevalley group in characteristic 2 or 3. This eliminates the distinction between the Suzuki–Ree groups over perfect and imperfect fields and gives a natural definition for the analogs of such groups over commutative rings. As an application of the same idea, we explicitly construct a pair of polynomial maps between the groups of types (Formula presented.) and (Formula presented.) in characteristic 2 that compose to the Frobenius endomorphism. This, in turn, provides a simple definition for the Tits mixed groups over rings.

KW - Suzuki—Ree groups

KW - Tits mixed groups

KW - Suzuki-Ree groups

KW - SUBGROUPS

UR - http://www.scopus.com/inward/record.url?scp=85074050336&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/95ac55ab-09c1-32e7-af1b-1069736236a6/

U2 - 10.1080/00927872.2019.1662913

DO - 10.1080/00927872.2019.1662913

M3 - Article

AN - SCOPUS:85074050336

VL - 48

SP - 815

EP - 825

JO - Communications in Algebra

JF - Communications in Algebra

SN - 0092-7872

IS - 2

ER -

ID: 71396468