Question in ABstract Algebra?

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Question in ABstract Algebra?

Given that 2 is a generator of the cyclic group U(25), how do you find all of the generators of U(25) listed as powers of 2???

2007-10-13 11:40:04 · 2 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics

2 answers

The GENERATORS are the elements whose orders are the same as the order of the group. Those would be the powers of two whose exponents are relatively prime to the order of the group.

I don't recognize the notation U(25), but if it's a group of order 24 then you're looking for powers of 2 where the exponent is divisible by neither 2 nor 3.

2007-10-13 13:42:24 · answer #1 · answered by Curt Monash 7 · 0⤊ 0⤋

That's easy: what are the powers of 2 in U(25)? They are 1, 2, 4, 8, 16, 7, 14, etc. (You finish it.)

2007-10-13 19:20:32 · answer #2 · answered by Anonymous · 1⤊ 2⤋