Let be a group and let be finite subgroups of relatively prime order. Prove that .
Let and . We saw in a previous exercise that is a subgroup of both and ; by Lagrange’s Theorem, then, divides and . Since , then, . Thus .
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Let be a group and let be finite subgroups of relatively prime order. Prove that .
Let and . We saw in a previous exercise that is a subgroup of both and ; by Lagrange’s Theorem, then, divides and . Since , then, . Thus .
On these pages you will find a slowly growing (and poorly organized) list of proofs and examples in abstract algebra.
No doubt these pages are riddled with typos and errors in logic, and in many cases alternate strategies abound. When you find an error, or if anything is unclear, let me know and I will fix it.