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

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10.1006/jabr.1996.0132

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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\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.",

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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.

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JO - Journal of Algebra

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ER -

Non-Abelian representations of some sporadic geometries

Abstract

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