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Find an example of sets of cosets of different cardinality

$G$ is a finite group. Let $H$ be a subgroup of $G$. Is there an example of $G$ and $H$ such that$${rm Card}({Hxhmid...

Mathematics Asked on 2 years ago

Prime number checker formula

First let $N = p^2$. I think that to show that any number less than $N$ is prime, you only have to check to show it has factors...

Mathematics Asked by Mondo Duke on 2 years ago

About holomorph of a finite group being the normalizer of regular image

Here is part of Exercise 5.5.19 in Dummit & Foote's Abstract Algebra:Let $H$ be a group of order $n$, let $K=operatorname{Aut}(H)$ and $G=operatorname{Hol}(H)=Hrtimes K$ (where ...

Mathematics Asked on 2 years ago

How do you generally tell the independence of events in a probability problem when it is not outright stated?

First question, do probability problems generally consisting of two categories always assume two events are dependent? Let's say there are two categories from a set of n people. They are...

Mathematics Asked on 2 years ago

Why this map is birational?

Let $Y$ be a connected normal Noetherian scheme, $f: Xto Y$ is an etale morphism of finite type. We assume $X$ is also connected. I have proved...

Mathematics Asked on 2 years ago

Relationship between multivariate Bernoulli random vector and categorical random variable

For simplicity, I'll focus on the bivariate case. Let $(X_1,X_2)$ be a random vector that obeys bivariate Bernoulli. $X_i$ takes either zero or one. The associated pdf can...

Mathematics Asked on 2 years ago

Can't argue with success? Looking for "bad math" that "gets away with it"

I'm looking for cases of invalid math operations producing (in spite of it all) correct results (aka "every math teacher's nightmare"). One example would be "cancelling" the 6's in ...

Mathematics Asked on 2 years ago

The topology generated by open intervals of rational numbers

Let$B = { mathbb{R} } cup { (a,b) capmathbb {Q} , alt b , a,b inmathbb{Q}}$ Thus, a set $V in B$...

Mathematics Asked by roslavets on 2 years ago

If the solutions of $X'=AX$ have a constant norm then $A$ is skew symmetric.

I have a differential equation $X'=AX$ where $Ainmathcal M_n(Bbb R)$. The question is to prove that if all the solutions have a constant norm then $A$ is skew-symmetric matrix. What...

Mathematics Asked by As soon as possible on 2 years ago

An interesting identity involving the abundancy index of divisors of odd perfect numbers

Let $sigma(x)$ denote the sum of divisors of the positive integer $x$. A number $y$ is said to be perfect if $sigma(y)=2y$. Denote the abundancy index...

Mathematics Asked on 2 years ago

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