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title is less overstated, since this is not about the converse in much generality

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edited Apr 16, 2011 at 17:12

DavidLHarden

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(A very limited instance of) Lagrange's Theorem's converse and A_5

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asked Apr 16, 2011 at 3:58

DavidLHarden

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Lagrange's Theorem's converse and A_5

Suppose $G$ is a finite simple group and $|G|$ is a multiple of $60$. Does it follow that $G$ has a subgroup isomorphic to $A_{5}$? If so, can this be proven without using the Classification?

gr.group-theory finite-groups