This is another problem from Herstein. The first problem 12 asks to prove that if G is closed under associative product and
(a) there is a e so that for any element a in G we have ae=a
(b) for each a in G there is a y(a) so that ay(a)=e
then G is a group. Although it took me some time to do...
counterexample so that (ab)^i=a^ib^i for two consecutive integers for any a and b in a group G does not imply that G is abelian.
this is a problem in herstein and I'm struggling to find an example. The previous problem to show that if (ab)^i=a^ib^i for 3 consecutive integers then G is...
Hi all, I'm looking for a positive real-valued function definition on all of R such that the function f(x) is continuous and integrable (the improper integral from -infinity to infinity exists and is finite) but that lim sup f(x)=infinity as x goes to infinity. I'm thinking about something with...
I was asked to show whether this is true: f(x) is defined for all x in [a,b] with f(b) > f(a) [values given]. the values of f at any x in (a,b) is rational. So, is f(x) continous?
I think this is not continuous as this seems like the question is trying to use intermediate value property to...
As a problem I was asked to show that phi, as defined by:
\phi_n(t) = \frac{n}{\pi(1+n^2t^2)}
Satisfies the property that for any f with the property to continuious at 0, then:
\lim_{n\rightarrow\infty} \int_{-\infty}^{\infty} \phi_n(t)f(t)dt = f(0)
But if we let f be 1/phi, we see that it...
Basically, I have to show an example such that for a nonabelian group G, with a,b elements of G, (a has order n, and b has order m), it is not necessarily the case that (ab)^mn= e. where e is the identity element.
im not sure where to start. =\