Search found 3 matches

by kotsos24919
Tue Dec 13, 2016 7:40 pm
Forum: Real Analysis
Topic: Existence of $x$
Replies: 1
Views: 2429

Existence of $x$

Let $A \subseteq \mathbb{R}^n$ be a compact and connected subset of $\mathbb{R}^n$. Suppose that $f:A \rightarrow \mathbb{R}$ is a continuous function and $g:A \rightarrow \mathbb{R}$ an integrable one. Prove that there exists an $x$ such that

$$\int \limits_A f g = f(x) \int \limits_A g $$
by kotsos24919
Sun Sep 04, 2016 11:15 am
Forum: Algebraic Structures
Topic: On Solvable Sylow groups
Replies: 1
Views: 2617

On Solvable Sylow groups

Let $p, q$ be prime numbers such that $p<q$ and let $G$ be a group such that $\left| G \right| =pq$.
  1. Prove that there exists a unique subgroup $H$ such that $\left| H \right| = q$.
  2. Prove that $H$ is a normal subgroup of $G$.
  3. Examine if $G$ is a solvable group.
by kotsos24919
Sat Aug 27, 2016 4:47 pm
Forum: Algebraic Structures
Topic: Groups
Replies: 1
Views: 2624

Groups

In $\mathbb{Z}$ we define $a*b=a$ . Prove that $(\mathbb{Z},*)$ isn't a group using the definition.