3. An algebraic structure F consists of the set of integers between 0 and 5 inclusive...

 

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3. An algebraic structure F consists of the set of integers between 0 and 5 inclusive (Z6), under the operation V, where a b = a + b + 3 (mod 6). a) Prove that F is a group? b) Evaluate the order of this group? c) Estimate the possible orders of subgroups that can be derived from this group, and find one of these subgroups (other than the 2 trivial subgroups). 3. An algebraic structure F consists of the set of integers between 0 and 5 inclusive (Z6), under the operation V, where a b = a + b + 3 (mod 6). a) Prove that F is a group? b) Evaluate the order of this group? c) Estimate the possible orders of subgroups that can be derived from this group, and find one of these subgroups (other than the 2 trivial subgroups).

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a To prove that the algebraic structure F is a group we need to show that it satisfies the four group axioms closure associativity identity element an... View the full answer