abstract algebra - If $G/Z (G)$ is cyclic, then $G$ is abelian ...
Therefore, G G is abelian. 1) Is this right so far? 2) How can I prove the "hint"?
How do you find the area of a parallelogram with the vertices?
Oct 13, 2016 · Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and …
How to show that the commutator subgroup is a normal subgroup
You don't need to figure out what a general element in the commutator subgroup looks like. The commutator subgroup is generated by commutators. Show that the property of "being a …
Understanding relationships between $L^1$ and $L^2$ spaces
Aug 9, 2020 · : L2 × L2 → R, with f, g = ∫Ifg. I also know that any inner product space is a normed space, and the norm is defined ‖f‖ = √ f, f . Given all of this, the part I am really not following is …
probability - How to calculate the odds of marble picking ...
Aug 11, 2022 · Imagine you have 9 marbles in a bag, 2 of them red, and 7 of them black. You pick a marble 3 times, replacing the marble after every pick. What is the probability that you pick …
Subgroup of index $2$ is Normal - Mathematics Stack Exchange
A subgroup is normal if and only if coset multiplication is well defined. The other group axioms aren't really in question (if the operation is well defined, they'll follow for free). Your argument …
trigonometry - Proving that $\cos (\arcsin (x))=\sqrt {1-x^2 ...
Jan 15, 2017 · I am asked to prove that $\\cos(\\arcsin(x)) = \\sqrt{1-x^2}$ I have used the trig identity to show that $\\cos^2(x) = 1 - x^2$ Therefore why isn't the answer denoted with the …
Prove that $\\gcd(a^n - 1, a^m - 1) = a^{\\gcd(n, m)} - 1$
Thus, by above aM − 1, aN − 1 and a (M, N) − 1 have the same set S of common divisors d, hence they have the same greatest common divisor (= max S) [same method as here]. Note …