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Leyli Jafari
Leyli Jafari
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Let $G$ be a nonabelian finite simple group, and let $p$ and $q$ be distinct prime divisors of the order of $G$. Is it true that the number of elements of $G$ of order $p$ never equals the number of elements of $G$ of order $q$?

Remark: My husband ran a GAP computation checking all nonabelian finite simple groups of order less than 30000000400000000, and did not find a counterexample.

Let $G$ be a nonabelian finite simple group, and let $p$ and $q$ be distinct prime divisors of the order of $G$. Is it true that the number of elements of $G$ of order $p$ never equals the number of elements of $G$ of order $q$?

Remark: My husband ran a GAP computation checking all nonabelian finite simple groups of order less than 30000000, and did not find a counterexample.

Let $G$ be a nonabelian finite simple group, and let $p$ and $q$ be distinct prime divisors of the order of $G$. Is it true that the number of elements of $G$ of order $p$ never equals the number of elements of $G$ of order $q$?

Remark: My husband ran a GAP computation checking all nonabelian finite simple groups of order less than 400000000, and did not find a counterexample.

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Leyli Jafari
Leyli Jafari
  • 347
  • 4
  • 13

Finite simple groups with the same numbers of elements of orders p and q

Let $G$ be a nonabelian finite simple group, and let $p$ and $q$ be distinct prime divisors of the order of $G$. Is it true that the number of elements of $G$ of order $p$ never equals the number of elements of $G$ of order $q$?

Remark: My husband ran a GAP computation checking all nonabelian finite simple groups of order less than 30000000, and did not find a counterexample.