(a) Give an example of a group which is abelian but not cyclic.

K4 right?

(b) Find 2^2005 in (non-zero elements)

(c) Find all solutions to the equation

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- Dec 27th 2007, 12:13 PMJason Bournegroups easy
(a) Give an example of a group which is abelian but not cyclic.

K4 right?

(b) Find 2^2005 in (non-zero elements)

(c) Find all solutions to the equation

- Dec 27th 2007, 12:31 PMThePerfectHacker
Yes.

Quote:

(b) Find 2^2005 in (non-zero elements)

Quote:

(c) Find all solutions to the equation

Thus, we require that for . Direct computation shows that is the only such exponent. Thus all the solutions have the form which can be writen as for .