Fixed point ratios in actions of finite exceptional groups of lie type.

School Of Mathematical Sciences

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Fixed point ratios in actions of finite exceptional groups of lie type. / Lawther, Ross; Liebeck, Martin W.; Seitz, Gary M.
In: Pacific Journal of Mathematics, Vol. 205, No. 2, 2002, p. 393-464.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Lawther, R, Liebeck, MW & Seitz, GM 2002, 'Fixed point ratios in actions of finite exceptional groups of lie type.', Pacific Journal of Mathematics, vol. 205, no. 2, pp. 393-464. <http://pjm.math.berkeley.edu/pjm/2002/205-2/p06.xhtml>

APA

Lawther, R., Liebeck, M. W., & Seitz, G. M. (2002). Fixed point ratios in actions of finite exceptional groups of lie type. Pacific Journal of Mathematics, 205(2), 393-464. http://pjm.math.berkeley.edu/pjm/2002/205-2/p06.xhtml

Vancouver

Lawther R, Liebeck MW, Seitz GM. Fixed point ratios in actions of finite exceptional groups of lie type. Pacific Journal of Mathematics. 2002;205(2):393-464.

Author

Lawther, Ross ; Liebeck, Martin W. ; Seitz, Gary M. / Fixed point ratios in actions of finite exceptional groups of lie type. In: Pacific Journal of Mathematics. 2002 ; Vol. 205, No. 2. pp. 393-464.

Bibtex

@article{53d619e7da404f55b60c6c76511cccca,

title = "Fixed point ratios in actions of finite exceptional groups of lie type.",

abstract = "Let G be a finite exceptional group of Lie type acting transitively on a set {\O}. For x in G, the fixed point ratio of x is the proportion of elements of {\O} which are fixed by x. We obtain new bounds for such fixed point ratios. When a point-stabilizer is parabolic we use character theory; and in other cases, we use results on an analogous problem for algebraic groups in Lawther, Liebeck & Seitz, 2002. These give dimension bounds on fixed point spaces of elements of exceptional algebraic groups, which we apply by passing to finite groups via a Frobenius morphism.",

author = "Ross Lawther and Liebeck, {Martin W.} and Seitz, {Gary M.}",

year = "2002",

language = "English",

volume = "205",

pages = "393--464",

journal = "Pacific Journal of Mathematics",

issn = "0030-8730",

publisher = "University of California, Berkeley",

number = "2",

}

RIS

TY - JOUR

T1 - Fixed point ratios in actions of finite exceptional groups of lie type.

AU - Lawther, Ross

AU - Liebeck, Martin W.

AU - Seitz, Gary M.

PY - 2002

Y1 - 2002

N2 - Let G be a finite exceptional group of Lie type acting transitively on a set Ø. For x in G, the fixed point ratio of x is the proportion of elements of Ø which are fixed by x. We obtain new bounds for such fixed point ratios. When a point-stabilizer is parabolic we use character theory; and in other cases, we use results on an analogous problem for algebraic groups in Lawther, Liebeck & Seitz, 2002. These give dimension bounds on fixed point spaces of elements of exceptional algebraic groups, which we apply by passing to finite groups via a Frobenius morphism.

AB - Let G be a finite exceptional group of Lie type acting transitively on a set Ø. For x in G, the fixed point ratio of x is the proportion of elements of Ø which are fixed by x. We obtain new bounds for such fixed point ratios. When a point-stabilizer is parabolic we use character theory; and in other cases, we use results on an analogous problem for algebraic groups in Lawther, Liebeck & Seitz, 2002. These give dimension bounds on fixed point spaces of elements of exceptional algebraic groups, which we apply by passing to finite groups via a Frobenius morphism.

M3 - Journal article

VL - 205

SP - 393

EP - 464

JO - Pacific Journal of Mathematics

JF - Pacific Journal of Mathematics

SN - 0030-8730

IS - 2

ER -

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