Finding involutions with small support

Alice C. Niemeyer; Tomasz Popiel

doi:10.1017/S0004972715001471

Finding involutions with small support

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Abstract

We show that the proportion of permutations g in S_n or A_nsuch that has even order and g_g/2is an involution with support of cardinality at most [m^ϵ] is at least a constant multiple of . Using this result, we obtain the same conclusion for elements in a classical group of natural dimension in odd characteristic that have even order and power up to an involution with (-1)-eigenspace of dimension at most [m^ϵ] for a linear or unitary group, or 2[n/2^ϵ]for a symplectic or orthogonal group.

Original language	English
Pages (from-to)	43-47
Number of pages	5
Journal	Bulletin of the Australian Mathematical Society
Volume	94
Issue number	1
DOIs	https://doi.org/10.1017/S0004972715001471
Publication status	Published - 1 Aug 2016
Externally published	Yes

Keywords

alternating group
classical group
involution
proportion of elements
symmetric group

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10.1017/S0004972715001471Licence: CC BY

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abstract = "We show that the proportion of permutations g in Sn or Ansuch that has even order and gg/2is an involution with support of cardinality at most [mϵ] is at least a constant multiple of . Using this result, we obtain the same conclusion for elements in a classical group of natural dimension in odd characteristic that have even order and power up to an involution with (-1)-eigenspace of dimension at most [mϵ] for a linear or unitary group, or 2[n/2ϵ]for a symplectic or orthogonal group.",

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AB - We show that the proportion of permutations g in Sn or Ansuch that has even order and gg/2is an involution with support of cardinality at most [mϵ] is at least a constant multiple of . Using this result, we obtain the same conclusion for elements in a classical group of natural dimension in odd characteristic that have even order and power up to an involution with (-1)-eigenspace of dimension at most [mϵ] for a linear or unitary group, or 2[n/2ϵ]for a symplectic or orthogonal group.

KW - alternating group

KW - classical group

KW - involution

KW - proportion of elements

KW - symmetric group

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Finding involutions with small support

Abstract

Keywords

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