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Community Bot
Community Bot
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This Wikipedia article states that the isomorphism type of a finite simple group is determined by its order, except that:

  • L4(2) and L3(4) both have order 20160
  • O2n+1(q) and S2n(q) have the same order for q odd, n > 2

I think this means that for each integer g, there are 0, 1 or 2 simple groups of order g.

Do we need the full strength of the Classification of Finite Simple Groups to prove this, or is there a simpler way of proving it?

(Originally asked at math.stackexchange.commath.stackexchange.com).

This Wikipedia article states that the isomorphism type of a finite simple group is determined by its order, except that:

  • L4(2) and L3(4) both have order 20160
  • O2n+1(q) and S2n(q) have the same order for q odd, n > 2

I think this means that for each integer g, there are 0, 1 or 2 simple groups of order g.

Do we need the full strength of the Classification of Finite Simple Groups to prove this, or is there a simpler way of proving it?

(Originally asked at math.stackexchange.com).

This Wikipedia article states that the isomorphism type of a finite simple group is determined by its order, except that:

  • L4(2) and L3(4) both have order 20160
  • O2n+1(q) and S2n(q) have the same order for q odd, n > 2

I think this means that for each integer g, there are 0, 1 or 2 simple groups of order g.

Do we need the full strength of the Classification of Finite Simple Groups to prove this, or is there a simpler way of proving it?

(Originally asked at math.stackexchange.com).

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Simon Nickerson
Simon Nickerson
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Number of finite simple groups of given order is at most 2 - is a classification-free proof possible?

This Wikipedia article states that the isomorphism type of a finite simple group is determined by its order, except that:

  • L4(2) and L3(4) both have order 20160
  • O2n+1(q) and S2n(q) have the same order for q odd, n > 2

I think this means that for each integer g, there are 0, 1 or 2 simple groups of order g.

Do we need the full strength of the Classification of Finite Simple Groups to prove this, or is there a simpler way of proving it?

(Originally asked at math.stackexchange.com).