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David Hill's user avatar
David Hill's user avatar
David Hill's user avatar
David Hill
  • Member for 10 years, 1 month
  • Last seen this week
47 votes
Accepted

Structure of groups of order $pq$, where $p,q$ are distinct primes.

14 votes

If $a$ is a transcendental number, then is $a^n$ also a transcendental number?

12 votes
Accepted

If $F$ is a field, then $F[x]$ is a principal ideal domain proof question

11 votes
Accepted

Coset multiplication giving a well defined binary operation

11 votes

Why aren't all functions considered a power function of 1 and integrated using some sort of chain rule?

11 votes

How are simple groups the building blocks?

10 votes
Accepted

Center of dihedral group

10 votes

Stuff which squares to $-1$ in the quaternions, thinking geometrically.

9 votes
Accepted

How can vector space $V\subsetneq W$ but $V\cong W$, where $V$ and $W$ don't have finite dimensions?

8 votes
Accepted

The group ring of a ring.

8 votes
Accepted

Computing information about a Lie algebra from cartan matrix

8 votes
Accepted

Automorphism group of $\mathbb{Q}$ considered as a group under addition

7 votes

Is the abelian nature of a group preserved under an isomorphism? Can we say the same thing for non-abelian groups?

7 votes
Accepted

Showing that $\mathbb{Z}[i]$ is not isomorphic to $\mathbb{Z}[\sqrt{2}]$

7 votes
Accepted

Semi direct product $G \cong N \rtimes_{\varphi} K $

6 votes
Accepted

If S $\subseteq G$ and $g \in G$, then $g N_G(S) g^{-1} = N_G ( g S g^{-1})$ and $g C_G(S) g^{-1} = C_G(gS g^{-1})$

6 votes

Meaning of this exercise in group theory

6 votes

Intersection of Maximal subgroups

5 votes

What is $\mathbb{Z}[x]/(x,x^2+1)$ isomorphic to?

5 votes

In any ring with unity, does $ab=1$ implies $ba=1$?

5 votes

$ gl(2,\mathbb C) \cong sl(2,\mathbb C) \oplus \mathbb C $

5 votes
Accepted

Finite dimensional division algebra over $\Bbb{C}$

5 votes
Accepted

Integral domains, polynomials and division

5 votes

Alternative proof: G group of order $p^2$, p prime $\Rightarrow$ $H$ is normal in $G$.

5 votes
Accepted

Centralizer (in $S_n$) of $ \sigma \in A_n $ such that its cycle decomposition contains only odd and different length cycles

5 votes

Is it true that $A_n$ contains all the elements of odd order?

4 votes

Let $(G,*)$ be a finite group and $a \in G$. Show that $\circ(a) \le |G|$.

4 votes
Accepted

How to find irreducible factors of the polynomial $p(x) = x^5 -1$ over integers modulo $5$

4 votes
Accepted

Understanding weight spaces of weight module from its composition factors?

4 votes
Accepted

Showing highest weight vectors are weight vectors

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