If Z is the centre of a group G, then show that a ∈ Z if and olny if N(a)=G, #abstract #algebra

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If a is the only element of order n in a group G, then show that a€Z(G)If a is the only element of order n in a group G, then show that a€Z(G)
Abstract Algebra 3.5: Center of a GroupAbstract Algebra 3.5: Center of a Group
(Abstract Algebra 1) The Center of a Group(Abstract Algebra 1) The Center of a Group
(Abstract Algebra 1) Definition of a Cyclic Group(Abstract Algebra 1) Definition of a Cyclic Group
|Z(G)| for |G|=pq|Z(G)| for |G|=pq
Abstract Algebra 9.5: G/Z TheoremAbstract Algebra 9.5: G/Z Theorem
Abstract Algebra | If G/Z(G) is cyclic then G is abelian.Abstract Algebra | If G/Z(G) is cyclic then G is abelian.
If the element a of a group G is of order n, then a ^ m = e iff n is a divisor of m. #mathematicsIf the element a of a group G is of order n, then a ^ m = e iff n is a divisor of m. #mathematics