Order of subgroup/

  • Thread starter arshavin
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  • #1
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If G is a group of order n, and n is divisible by k. Then must G have a subgroup of order k?

proof or counterexamples?
 

Answers and Replies

  • #2
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No - one reason to see immediately why, is because if it was true, then Lagrange's theorem should be a two way implication.

Simplest example via wikipedia is [tex]\mathbb{A}_4[/tex] with has order 12 and no subgroup of order 6.
 
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