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Involutions of the Mathieu groups Fraser, Richard Evan James
Abstract
The five Mathieu permutation groups M₁₁, M₁₂M₂₂,M₂₃ and M₂₄ are constructed and the involutions (elements of order two) of these groups are classified according to the number of letters they fix. It is shown that in M₁₂ ah involution fixes no letters or four letters, while in M₂₄ an involution fixes zero or eight letters. It is also shown that in each of the Mathieu groups, all the irregular involutions are conjugate and that in M₁₂ all the regular involutions are conjugate. The orders of the centralizers of the involutions are calculated and it is shown that no regular involution lies in the centre of a 2-Sylow subgroup. Most of the results are obtained by calculating directly the form a permutation must take in order to have a certain property and then finding one or all the permutations of this form.
Item Metadata
Title |
Involutions of the Mathieu groups
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Creator | |
Publisher |
University of British Columbia
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Date Issued |
1966
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Description |
The five Mathieu permutation groups M₁₁, M₁₂M₂₂,M₂₃ and M₂₄ are constructed and the involutions (elements of order two) of these groups are classified according to the number of letters they fix. It is shown that in M₁₂ ah involution fixes no letters or four letters, while in M₂₄ an involution fixes zero or eight letters. It is also shown that in each of the Mathieu groups, all the irregular involutions are conjugate and that in M₁₂ all the regular involutions are conjugate. The orders of the centralizers of the involutions are calculated and it is shown that no regular involution lies in the centre of a 2-Sylow subgroup.
Most of the results are obtained by calculating directly the form a permutation must take in order to have a certain property and then finding one or all the permutations of this form.
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Genre | |
Type | |
Language |
eng
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Date Available |
2011-10-13
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Provider |
Vancouver : University of British Columbia Library
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Rights |
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.
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DOI |
10.14288/1.0080539
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URI | |
Degree | |
Program | |
Affiliation | |
Degree Grantor |
University of British Columbia
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Campus | |
Scholarly Level |
Graduate
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Aggregated Source Repository |
DSpace
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Rights
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.