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A note on the probability of generating alternating or symmetric groups

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A note on the probability of generating alternating or symmetric groups. / Morgan, Luke; Roney-Dougal, Colva Mary.

In: Archiv der Mathematik, Vol. 105, No. 3, 09.2015, p. 201-204.

Research output: Contribution to journalArticlepeer-review

Harvard

Morgan, L & Roney-Dougal, CM 2015, 'A note on the probability of generating alternating or symmetric groups', Archiv der Mathematik, vol. 105, no. 3, pp. 201-204. https://doi.org/10.1007/s00013-015-0796-8

APA

Morgan, L., & Roney-Dougal, C. M. (2015). A note on the probability of generating alternating or symmetric groups. Archiv der Mathematik, 105(3), 201-204. https://doi.org/10.1007/s00013-015-0796-8

Vancouver

Morgan L, Roney-Dougal CM. A note on the probability of generating alternating or symmetric groups. Archiv der Mathematik. 2015 Sep;105(3):201-204. https://doi.org/10.1007/s00013-015-0796-8

Author

Morgan, Luke ; Roney-Dougal, Colva Mary. / A note on the probability of generating alternating or symmetric groups. In: Archiv der Mathematik. 2015 ; Vol. 105, No. 3. pp. 201-204.

Bibtex - Download

@article{45c657540e874df3a9911fc5d974ce52,
title = "A note on the probability of generating alternating or symmetric groups",
abstract = "We improve on recent estimates for the probability of generating the alternating and symmetric groups An and Sn. In particular, we find the sharp lower bound if the probability is given by a quadratic in n−1. This leads to improved bounds on the largest number h(An) such that a direct product of h(An) copies of An can be generated by two elements.",
keywords = "Symmetric group, Alternating group, Generation, Probability",
author = "Luke Morgan and Roney-Dougal, {Colva Mary}",
note = "The research of the first author is supported by the Australian Research Council grant DP120100446. ",
year = "2015",
month = sep,
doi = "10.1007/s00013-015-0796-8",
language = "English",
volume = "105",
pages = "201--204",
journal = "Archiv der Mathematik",
issn = "0003-889X",
publisher = "Birkhauser Verlag Basel",
number = "3",

}

RIS (suitable for import to EndNote) - Download

TY - JOUR

T1 - A note on the probability of generating alternating or symmetric groups

AU - Morgan, Luke

AU - Roney-Dougal, Colva Mary

N1 - The research of the first author is supported by the Australian Research Council grant DP120100446.

PY - 2015/9

Y1 - 2015/9

N2 - We improve on recent estimates for the probability of generating the alternating and symmetric groups An and Sn. In particular, we find the sharp lower bound if the probability is given by a quadratic in n−1. This leads to improved bounds on the largest number h(An) such that a direct product of h(An) copies of An can be generated by two elements.

AB - We improve on recent estimates for the probability of generating the alternating and symmetric groups An and Sn. In particular, we find the sharp lower bound if the probability is given by a quadratic in n−1. This leads to improved bounds on the largest number h(An) such that a direct product of h(An) copies of An can be generated by two elements.

KW - Symmetric group

KW - Alternating group

KW - Generation

KW - Probability

U2 - 10.1007/s00013-015-0796-8

DO - 10.1007/s00013-015-0796-8

M3 - Article

VL - 105

SP - 201

EP - 204

JO - Archiv der Mathematik

JF - Archiv der Mathematik

SN - 0003-889X

IS - 3

ER -

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