Caleb Shor

@cshor.org

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* Math professor at WNEU * Director of PROMYS for Teachers at Boston University * Travel enthusiast * Fan of lists

Me: What is the smallest group whose order is a power of 2 that has no normal subgroup of order 2? It: Every nontrivial 2-group has a nontrivial center, and any element of order 2 in the center generates a normal subgroup of order 2. In particular, by the class-equation argument, every 2-group has a normal subgroup of order 2. Hence there is no (nontrivial) 2-group whose order is a power of 2 and yet has no normal subgroup of order 2.