Embeddings of L(2,13) in groups of Lie type of E6

A.M. Cohen; D.B. Wales

doi:10.1007/BF02808108

Embeddings of L(2,13) in groups of Lie type of E6

A.M. Cohen, D.B. Wales

Discrete Algebra and Geometry

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

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Abstract

In this paper we show there is exactly one conjugacy class of subgroups ofE 6(C) isomorphic toL(2, 13) with each of the characters 13+14 and 1+12+14 on a 27-dimensional module forE 6. The one with character 13+14 is a subgroup of the irreducible closed subgroup of typeG 2. There is a unique conjugacy class for each of the three algebraic conjugate characters 1+12+14. Our arguments have applications to fields of characteristic prime to |L(2, 13)|.

Original language	English
Pages (from-to)	45-86
Journal	Israel Journal of Mathematics
Volume	82
DOIs	https://doi.org/10.1007/BF02808108
Publication status	Published - 1993

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title = "Embeddings of L(2,13) in groups of Lie type of E6",

abstract = "In this paper we show there is exactly one conjugacy class of subgroups ofE 6(C) isomorphic toL(2, 13) with each of the characters 13+14 and 1+12+14 on a 27-dimensional module forE 6. The one with character 13+14 is a subgroup of the irreducible closed subgroup of typeG 2. There is a unique conjugacy class for each of the three algebraic conjugate characters 1+12+14. Our arguments have applications to fields of characteristic prime to |L(2, 13)|.",

author = "A.M. Cohen and D.B. Wales",

year = "1993",

doi = "10.1007/BF02808108",

language = "English",

volume = "82",

pages = "45--86",

journal = "Israel Journal of Mathematics",

issn = "0021-2172",

publisher = "Springer",

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T1 - Embeddings of L(2,13) in groups of Lie type of E6

AU - Cohen, A.M.

AU - Wales, D.B.

PY - 1993

Y1 - 1993

N2 - In this paper we show there is exactly one conjugacy class of subgroups ofE 6(C) isomorphic toL(2, 13) with each of the characters 13+14 and 1+12+14 on a 27-dimensional module forE 6. The one with character 13+14 is a subgroup of the irreducible closed subgroup of typeG 2. There is a unique conjugacy class for each of the three algebraic conjugate characters 1+12+14. Our arguments have applications to fields of characteristic prime to |L(2, 13)|.

AB - In this paper we show there is exactly one conjugacy class of subgroups ofE 6(C) isomorphic toL(2, 13) with each of the characters 13+14 and 1+12+14 on a 27-dimensional module forE 6. The one with character 13+14 is a subgroup of the irreducible closed subgroup of typeG 2. There is a unique conjugacy class for each of the three algebraic conjugate characters 1+12+14. Our arguments have applications to fields of characteristic prime to |L(2, 13)|.

U2 - 10.1007/BF02808108

DO - 10.1007/BF02808108

M3 - Article

VL - 82

SP - 45

EP - 86

JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

SN - 0021-2172

ER -