1. In each case, determine whether * is associative, whether * has an identity element and, if the latter is the case, whether each element of S has an inverse (with regards to *), ie whether S is a group:
(a) S={1,-1}, * ordinary multiplication of integers
(b) S= the subset of Q consisting of all positive rationals that have a rational square roots, *=ordinary multiplication of rationals
(c) S=R\{0}, the set of all non-zero reals with a*b=|ab|
2. From examples above that are groups, which are abelian?
3. Consider groups Z(subscript n) with binary operation being addition modulo n. Write down operation tables for
(a) n=4,5
(b) n=6
4.Prove that if G=, then G=
5. Let G be a finite group, and let g,x∈ G
(a) prove that x and g^-1xg have the same order
(b) Let a,b∈G. Prove that ab and ba have the same order
This is exam revision. I really appreciate the help. if possible i need full working out and explinations.
Thanks
Don
2007-10-18
19:15:33
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1 answers
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Anonymous
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Mathematics