International Journal of Statistics and Applied Mathematics
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International Journal of Statistics and Applied Mathematics

2021, Vol. 6, Issue 4, Part A

Analysis on generating transitive permutation group


Author(s): Manish Kumar Gupta and Dr. Ashok Kumar

Abstract: Denote by f(n) the number of subgroups of the symmetric group Sym(n) of degree n, and by ftrans(n) the number of its transitive subgroups. It was conjectured by Pyber that almost all subgroups of Sym(n) are not transitive, that is, ftrans(n)/f(n) tends to 0 when n tends to infinity. It is still an open question whether or not this conjecture is true. The difficulty comes from the fact that, from many points of view, transitivity is not a really strong restriction on permutation groups, and there are too many transitive groups. In paper paper we solve the problem in the particular case of permutation groups of prime power degree, proving the following result.

Pages: 25-29 | Views: 37 | Downloads: 5

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How to cite this article:
Manish Kumar Gupta, Dr. Ashok Kumar. Analysis on generating transitive permutation group. Int J Stat Appl Math 2021;6(4):25-29.
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