Question
Prove that $A_{5}$ has no subgroup of order 15 to $20 .$
Step 1
Suppose $A_5$ has a subgroup $H$ of order 15. Then, by Lagrange's theorem, the order of any element in $H$ must divide 15. Thus, the possible orders of elements in $H$ are 1, 3, and 5. Show more…
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