Non-Abelian representations of some sporadic geometries

Alexander A. Ivanov; Dmitrii V. Pasechnik; Sergey V. Shpectorov

doi:10.1006/jabr.1996.0132

Non-Abelian representations of some sporadic geometries

Alexander A. Ivanov^*
, Dmitrii V. Pasechnik
, Sergey V. Shpectorov

^*Corresponding author for this work

Mathematics

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

Abstract

For a point-line incidence system script I = (P,L) with three points per line we define the universal representation group of ℐ as R(ℐ) = 〈z_p, p ∈ P\z²_p = 1 for p ∈ P, z_pz_qz_r = 1 for {p,q,r} ∈ L〉. We prove that if script G is the 2-local parabolic geometry of the sporadic simple group F₁ (the Monster) or F₂ (the Baby Monster) then R(script G) ≅ F₁ or 2 · F₂, respectively.

Original language	English
Pages (from-to)	523-557
Number of pages	35
Journal	Journal of Algebra
Volume	181
Issue number	2
DOIs	https://doi.org/10.1006/jabr.1996.0132
Publication status	Published - 15 Apr 1996

ASJC Scopus subject areas

Algebra and Number Theory

Access to Document

10.1006/jabr.1996.0132

Cite this

@article{fc194c7e0974441bb42596a8748c3b4d,

title = "Non-Abelian representations of some sporadic geometries",

abstract = "For a point-line incidence system script I = (P,L) with three points per line we define the universal representation group of ℐ as R(ℐ) = 〈zp, p ∈ P\textbackslash{}z2p = 1 for p ∈ P, zpzqzr = 1 for \{p,q,r\} ∈ L〉. We prove that if script G is the 2-local parabolic geometry of the sporadic simple group F1 (the Monster) or F2 (the Baby Monster) then R(script G) ≅ F1 or 2 · F2, respectively.",

author = "Ivanov, \{Alexander A.\} and Pasechnik, \{Dmitrii V.\} and Shpectorov, \{Sergey V.\}",

year = "1996",

month = apr,

day = "15",

doi = "10.1006/jabr.1996.0132",

language = "English",

volume = "181",

pages = "523--557",

journal = "Journal of Algebra",

issn = "0021-8693",

publisher = "Elsevier",

number = "2",

}

TY - JOUR

T1 - Non-Abelian representations of some sporadic geometries

AU - Ivanov, Alexander A.

AU - Pasechnik, Dmitrii V.

AU - Shpectorov, Sergey V.

PY - 1996/4/15

Y1 - 1996/4/15

N2 - For a point-line incidence system script I = (P,L) with three points per line we define the universal representation group of ℐ as R(ℐ) = 〈zp, p ∈ P\z2p = 1 for p ∈ P, zpzqzr = 1 for {p,q,r} ∈ L〉. We prove that if script G is the 2-local parabolic geometry of the sporadic simple group F1 (the Monster) or F2 (the Baby Monster) then R(script G) ≅ F1 or 2 · F2, respectively.

AB - For a point-line incidence system script I = (P,L) with three points per line we define the universal representation group of ℐ as R(ℐ) = 〈zp, p ∈ P\z2p = 1 for p ∈ P, zpzqzr = 1 for {p,q,r} ∈ L〉. We prove that if script G is the 2-local parabolic geometry of the sporadic simple group F1 (the Monster) or F2 (the Baby Monster) then R(script G) ≅ F1 or 2 · F2, respectively.

UR - https://www.scopus.com/pages/publications/0000294795

U2 - 10.1006/jabr.1996.0132

DO - 10.1006/jabr.1996.0132

M3 - Article

AN - SCOPUS:0000294795

SN - 0021-8693

VL - 181

SP - 523

EP - 557

JO - Journal of Algebra

JF - Journal of Algebra

IS - 2

ER -

Non-Abelian representations of some sporadic geometries

Abstract

ASJC Scopus subject areas

Access to Document

Fingerprint

Cite this