A proper subgroup H of a group G is called maximal if
Chapter 9, Problem 78E(choose chapter or problem)
A proper subgroup H of a group G is called maximal if there is no subgroup K such that \(H \subset K \subset G\) (that is, there is no subgroup K properly contained between H and $G)$. Show that Z(G) is never a maximal subgroup of a group G.
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