The probability that two elements of a finite nonabelian simple group commute

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It is mentioned in here (last paragraph of the first page) that Dixon proved the following result: the probability that two elements of a finite nonabelian simple group commute is at most $frac112$. I cannot seem to find this proof anywhere online. Do you know a proof of this fact? Or do you have a reference for it? (I am actually more interested in the original proof)






reference-request gr.group-theory pr.probability finite-groups







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    In fact, for any $epsilon$, there will be at most finitely many simple groups $G$ with $cp(G) geq epsilon$. This follows from Dixon's argument (linked below) and the fact that for any $n$ there are at most finitely many finite simple groups with an irreducible representation of dimension $n$. See e.g. mathoverflow.net/a/27365/1345
    – Ian Agol
    3 hours ago














up vote
3
down vote

favorite












It is mentioned in here (last paragraph of the first page) that Dixon proved the following result: the probability that two elements of a finite nonabelian simple group commute is at most $frac112$. I cannot seem to find this proof anywhere online. Do you know a proof of this fact? Or do you have a reference for it? (I am actually more interested in the original proof)






reference-request gr.group-theory pr.probability finite-groups







share|cite|improve this question









New contributor




user129021 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.















  • 1




    In fact, for any $epsilon$, there will be at most finitely many simple groups $G$ with $cp(G) geq epsilon$. This follows from Dixon's argument (linked below) and the fact that for any $n$ there are at most finitely many finite simple groups with an irreducible representation of dimension $n$. See e.g. mathoverflow.net/a/27365/1345
    – Ian Agol
    3 hours ago












up vote
3
down vote

favorite









up vote
3
down vote

favorite











It is mentioned in here (last paragraph of the first page) that Dixon proved the following result: the probability that two elements of a finite nonabelian simple group commute is at most $frac112$. I cannot seem to find this proof anywhere online. Do you know a proof of this fact? Or do you have a reference for it? (I am actually more interested in the original proof)






reference-request gr.group-theory pr.probability finite-groups







share|cite|improve this question









New contributor




user129021 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











It is mentioned in here (last paragraph of the first page) that Dixon proved the following result: the probability that two elements of a finite nonabelian simple group commute is at most $frac112$. I cannot seem to find this proof anywhere online. Do you know a proof of this fact? Or do you have a reference for it? (I am actually more interested in the original proof)






reference-request gr.group-theory pr.probability finite-groups




reference-request gr.group-theory pr.probability finite-groups






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edited 2 hours ago









Yemon Choi

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  • 1




    In fact, for any $epsilon$, there will be at most finitely many simple groups $G$ with $cp(G) geq epsilon$. This follows from Dixon's argument (linked below) and the fact that for any $n$ there are at most finitely many finite simple groups with an irreducible representation of dimension $n$. See e.g. mathoverflow.net/a/27365/1345
    – Ian Agol
    3 hours ago












  • 1




    In fact, for any $epsilon$, there will be at most finitely many simple groups $G$ with $cp(G) geq epsilon$. This follows from Dixon's argument (linked below) and the fact that for any $n$ there are at most finitely many finite simple groups with an irreducible representation of dimension $n$. See e.g. mathoverflow.net/a/27365/1345
    – Ian Agol
    3 hours ago







1




1




In fact, for any $epsilon$, there will be at most finitely many simple groups $G$ with $cp(G) geq epsilon$. This follows from Dixon's argument (linked below) and the fact that for any $n$ there are at most finitely many finite simple groups with an irreducible representation of dimension $n$. See e.g. mathoverflow.net/a/27365/1345
– Ian Agol
3 hours ago




In fact, for any $epsilon$, there will be at most finitely many simple groups $G$ with $cp(G) geq epsilon$. This follows from Dixon's argument (linked below) and the fact that for any $n$ there are at most finitely many finite simple groups with an irreducible representation of dimension $n$. See e.g. mathoverflow.net/a/27365/1345
– Ian Agol
3 hours ago










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You can find Dixon's argument here (Google Books). (J.D..Dixon, Solution to Problem 176, Canadian Mathematical Bulletin 16 (1973), p302.)






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    You can find Dixon's argument here (Google Books). (J.D..Dixon, Solution to Problem 176, Canadian Mathematical Bulletin 16 (1973), p302.)






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      You can find Dixon's argument here (Google Books). (J.D..Dixon, Solution to Problem 176, Canadian Mathematical Bulletin 16 (1973), p302.)






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        You can find Dixon's argument here (Google Books). (J.D..Dixon, Solution to Problem 176, Canadian Mathematical Bulletin 16 (1973), p302.)






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        You can find Dixon's argument here (Google Books). (J.D..Dixon, Solution to Problem 176, Canadian Mathematical Bulletin 16 (1973), p302.)







        share|cite|improve this answer














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