3. Define Lie group.
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- Let be a subgroup of a group with . Prove that if and only if31. (See Exercise 30.) Prove that if and are primes and is a nonabelian group of order , then the center of is the trivial subgroup . Exercise 30: 30. Let be a group with center . Prove that if is cyclic, then is abelian.18. If is a subgroup of the group such that for all left cosets and of in, prove that is normal in.