36) Prove that if G/Z(G) is cyclic then G is abelian. [If G /Z(G) is cyclic with generator xZ(G), show that every element of G can be written in the form xaz for some integer a E Z and some element z E Z(G).]

36) Prove that if G/Z(G) is cyclic then G is abelian. [If G /Z(G) is cyclic with generator xZ(G), show that every element of G can be written in the form xaz for some integer a E Z and some element z E Z(G).]

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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36) Prove that if G/Z (G) is cyclic then G is abelian. [If G/Z (G) is cyclic with generator xZ (G), show that
every element of G can be written in the form x"z for some integer a E Z and some element z E Z(G).]

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