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Journal of Group Theory

Editor-in-Chief: Parker, Christopher W.

Managing Editor: Wilson, John S. / Khukhro, Evgenii I. / Kramer, Linus


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Online
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1435-4446
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Volume 15, Issue 6

Issues

Proportions of elements with given 2-part order in the symmetric group

Simon Guest
  • Centre for the Mathematics of Symmetry and Computation (M019), The University of Western Australia, 35 Stirling Highway, Crawley WA 6009, Australia. [1mm]Current address: School of Mathematics, University of Southampton, Southampton, SO17 1BJ, UK
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/ Cheryl E. Praeger
  • Centre for the Mathematics of Symmetry and Computation (M019), The University of Western Australia, 35 Stirling Highway, Crawley WA 6009, Australia; and King Abdulaziz University, Jeddah, Saudi Arabia
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Published Online: 2012-11-01 | DOI: https://doi.org/10.1515/jgt-2012-0021

Abstract.

For an element g in a group X, we say that g has 2-part order if is the largest power of 2 dividing the order of g. Using results of Erdős and Turán, and Beals et al., we give explicit lower bounds on the proportion of elements of the symmetric group with certain 2-part orders. Some of these lower bounds are constant; for example we show that at least 23.5% of the elements in () have a certain 2-part order and furthermore, more than half of the elements in have one of three 2-part orders. Also, for all , at least of the elements in have the same 2-part order and we show that is best possible.

About the article

Received: 2012-05-20

Revised: 2012-05-27

Published Online: 2012-11-01

Published in Print: 2012-11-01


Citation Information: Journal of Group Theory, Volume 15, Issue 6, Pages 717–735, ISSN (Online) 1435-4446, ISSN (Print) 1433-5883, DOI: https://doi.org/10.1515/jgt-2012-0021.

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© 2012 by Walter de Gruyter Berlin Boston.Get Permission

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