OK, I got that the gcd(n,m)|(a-b)-> x==a mod(n) and x==b mod(m) will have a solution, but showing that that solution is restricted to the modulus of m*n is giving me troubles...
Hello,
I am looking into proving that the Chinese Remainder Theorem will work for two pairs of congruences IFF a congruent to b modulo(gcd(n,m)) for
x congruent to a mod(n) and x congruent to b mod(m).
I have gotten one direction, that given a solution to the congruences mod(m*n), then a...
Hello,
If we are given that b3|a2, how do we show that b|a?
I started off looking at prime factorizations, but I could use a push in a more substantial direction.
The permutation group S_3.
I looked at this also... but the cubes of the individual elements seemed closed under the operation of composition, and the identity is present... Four of us have spent about 3 hours on this without much luck, any nudging is greatly appreciated!
Homework Statement
Let G be an Abelian group and let H+{x^3 : x is an element of G}
Find a non-Abelian group in which H is not a subgroup
Homework Equations
I wish it was that easy...
The Attempt at a Solution
I looked at the quaternion group, and some other matrix groups, but...