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December 24, 2021 9:42 pm 30 pts
40. Let G be a group with identity e. Let H be an abelian non-trivial proper subgroup of G with the property that H n gHg = {e} for all ge H. If K = {geG:gh = hg for all he H}, then (a) K is a proper subgroup of H (b) H is a proper subgroup of K (c) K = H (d) there exists no abelian subgroup LcG such that K is a proper subgroup of L
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