Let G be a group and let Z(G) be the centre of G.(i)What is an alternative way of saying Z(G) = G?(ii) = 6 and Z(G) + {e}. Give an example ofGive an example of a group G such that Ga group G such that |G| = 6 and Z(G) = {e}. (No proofs are required.)(i)Does there exist a group G such that |G| > 2 but |Z(G)| = 2? Give an example, orprove that such a group does not exist.(iv) Does there exist a group G such that the index of Z(G) in G is 2? Give an example, orprove that such a group does not exist.

As it is a multiple part question , so I am solving the first three subparts only, if more subpart…

Let G be a group and let Z(G) be the centre of G. (i) What is an alternative way of saying Z(G) = G? (ii) Give an example of a group G such that |G| = 6 and Z(G) + {e}. Give an example of a group G such that |G| = 6 and Z(G) = {e}. (No proofs are required.) (iii) Does there exist a group G such that |G| > 2 but |Z(G)| = 2? Give an example, or %3D prove that such a group does not exist.

Let G be a group and let Z(G) be the centre of G. (i) What is an alternative way of saying Z(G) = G? (ii) Give an example of a group G such that |G| = 6 and Z(G) + {e}. Give an example of a group G such that |G| = 6 and Z(G) = {e}. (No proofs are required.) (iii) Does there exist a group G such that |G| > 2 but |Z(G)| = 2? Give an example, or %3D prove that such a group does not exist.

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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