Asymptotics of the number of involutions in finite classical groups

Jason Fulman; Robert Guralnick; Dennis Stanton; Gunter Malle

doi:10.1515/jgth-2017-0011

Asymptotics of the number of involutions in finite classical groups

Jason Fulman, Robert Guralnick, Dennis Stanton, Gunter Malle

Mathematics

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

6 Scopus citations

Abstract

Answering a question of Geoff Robinson, we compute the large n limiting proportion of i_GL(n, q)=q^[n2=2], where i_GL(n, q) denotes the number of involutions in the group GL(n, q). We give similar results for the finite unitary, symplectic, and orthogonal groups, in both odd and even characteristic. At the heart of this work are certain new "sum = product" identities. Our self-contained treatment of the enumeration of involutions in even characteristic symplectic and orthogonal groups may also be of interest.

Original language	English (US)
Pages (from-to)	871-902
Number of pages	32
Journal	Journal of Group Theory
Volume	20
Issue number	5
DOIs	https://doi.org/10.1515/jgth-2017-0011
State	Published - Sep 1 2017

Bibliographical note

Funding Information:
Fulman was partially supported by Simons Foundation Grant 400528. Guralnick was partially supported by NSF grants DMS-1302886 and DMS-1600056. Stanton was partially supported by NSF grant DMS-1148634.

Publisher Copyright:
© de Gruyter 2017.

Access

10.1515/jgth-2017-0011

Cite this

@article{45fd5e750f5f4ebb888db9bc1b74a0ef,

title = "Asymptotics of the number of involutions in finite classical groups",

abstract = "Answering a question of Geoff Robinson, we compute the large n limiting proportion of iGL(n, q)=q[n2=2], where iGL(n, q) denotes the number of involutions in the group GL(n, q). We give similar results for the finite unitary, symplectic, and orthogonal groups, in both odd and even characteristic. At the heart of this work are certain new {"}sum = product{"} identities. Our self-contained treatment of the enumeration of involutions in even characteristic symplectic and orthogonal groups may also be of interest.",

author = "Jason Fulman and Robert Guralnick and Dennis Stanton and Gunter Malle",

note = "Funding Information: Fulman was partially supported by Simons Foundation Grant 400528. Guralnick was partially supported by NSF grants DMS-1302886 and DMS-1600056. Stanton was partially supported by NSF grant DMS-1148634. Publisher Copyright: {\textcopyright} de Gruyter 2017.",

year = "2017",

month = sep,

day = "1",

doi = "10.1515/jgth-2017-0011",

language = "English (US)",

volume = "20",

pages = "871--902",

journal = "Journal of Group Theory",

issn = "1433-5883",

publisher = "Walter de Gruyter GmbH & Co. KG",

number = "5",

}

TY - JOUR

T1 - Asymptotics of the number of involutions in finite classical groups

AU - Fulman, Jason

AU - Guralnick, Robert

AU - Stanton, Dennis

AU - Malle, Gunter

N1 - Funding Information: Fulman was partially supported by Simons Foundation Grant 400528. Guralnick was partially supported by NSF grants DMS-1302886 and DMS-1600056. Stanton was partially supported by NSF grant DMS-1148634. Publisher Copyright: © de Gruyter 2017.

PY - 2017/9/1

Y1 - 2017/9/1

N2 - Answering a question of Geoff Robinson, we compute the large n limiting proportion of iGL(n, q)=q[n2=2], where iGL(n, q) denotes the number of involutions in the group GL(n, q). We give similar results for the finite unitary, symplectic, and orthogonal groups, in both odd and even characteristic. At the heart of this work are certain new "sum = product" identities. Our self-contained treatment of the enumeration of involutions in even characteristic symplectic and orthogonal groups may also be of interest.

AB - Answering a question of Geoff Robinson, we compute the large n limiting proportion of iGL(n, q)=q[n2=2], where iGL(n, q) denotes the number of involutions in the group GL(n, q). We give similar results for the finite unitary, symplectic, and orthogonal groups, in both odd and even characteristic. At the heart of this work are certain new "sum = product" identities. Our self-contained treatment of the enumeration of involutions in even characteristic symplectic and orthogonal groups may also be of interest.

UR - http://www.scopus.com/inward/record.url?scp=85028809040&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85028809040&partnerID=8YFLogxK

U2 - 10.1515/jgth-2017-0011

DO - 10.1515/jgth-2017-0011

M3 - Article

AN - SCOPUS:85028809040

VL - 20

SP - 871

EP - 902

JO - Journal of Group Theory

JF - Journal of Group Theory

SN - 1433-5883

IS - 5

ER -

Asymptotics of the number of involutions in finite classical groups

Abstract

Bibliographical note

Access

Other files and links

Fingerprint

Cite this