if G is a group such that (xy)^{3} = x^{3}y^{3} for all x,y in G, and if 3 does not divide the order of G, then G is abelian.
I proved an earlier result that said if there exists an n such that
(xy)^{n} = x^{n}y^{n}
(xy)^{n+1} = x^{n+1}y^{n+1}
(xy)^{n+2} = x^{n+2}y^{n+2} for all x,y in G...
Without Sylow's theorems!!
This was a problem at the end of a chapter on Lagrange's theorem. I know that every subgroup of order 77 is cyclic. But I don't know how to prove this using only Lagrange. Any suggestions?
I know that Euler is pronounced Oiler, and Galois is Gale-Wah. Can anyone try to write phonetically Stieltjes, Lebesgue or any other mathematicians whose names which may be tricky.
in the book i'm reading it gives a set S={0,1,2,3}, and it says that the relation R where (m,n) \in R if m + n = 3, m,n \in S.
it says that this relation isn't transitive, but couldn't you give a vacuous argument for transitivity.
more specifically there are no x,y,z s.t. (x,y) and (y,z)...
right now i work as a cashier at home depot, and i feel like i can do better for a part time job. does anyone have advice for the type of job i can get with an associates in math/science while still in school.
i'm reading shilov's "real and complex analysis". there is a problem to prove that for real positive x1,x2,...xn, if x1*x2*...*xn=1, then x1+x2+...xn >= n. I proved this for the case n = 2. it says use induction on this case to prove it for the nth case. but i just don't see it.
for n=2...
I'm transferring from at two year school to a four year school to get my bachelors in math. In order to get the degree, I need to take a language other than english. Does anyone have any input as to what language would be best to learn as far as mathematics go. I was thinking probably german...