Recent content by zcahana

Thanks for you help!...

Sorry... I still see a problem with the conclusion that mn divides |G|...

Thanks for the response. By stating that M\capN = <1> did you mean M\capN = e? If so, it seems to me that it is not necessarily true. If you meant something else, please elaborate.Zvi.

Yes I did, sorry for the mistake... *Corrected*

Homework Statement Let G be a finite group and N\triangleleftG such that |N| = n, and gcd(n,[G:N]) = 1. Proof that if x^{n} = e then x\inN. Homework Equations none. The Attempt at a Solution I defined |G| = m and and tried to find an integer which divides both n and m/n. I went for some X...

Ok, For a. , I concluded that if f(x) = 2 then f(x/2) = sqrt(2) , with contradiction to that f(x/2) is (positive) rational. For b. , proved. For c. , I marked s = (1,2)(3,4,5)(6,7,8,9,10) , o(s) = 30 and for any x in Z30, f(x) = s^x such that IM(f) = <s> , and f(x) is well defined because...

Homework Statement The exercise is to find examples of various homomorphisms from/to various groups. Those I'm having problems with are: a. f: (Q,+) --> (Q^+,*) which is onto. b. f: U20 --> Z64 which is 1-to-1. c. f: Z30 --> S10 which is 1-to-1. Homework Equations The Attempt...