# Tagged Questions

**4**

votes

**1**answer

162 views

### Cyclic subgroups of GL(n,q)

Let $q$ be a prime power. It is well known that every Singer subgroup (subgroup of order $q^n-1$) in $GL(n,q)$ are conjugate. My question is: If $H$ is a cyclic subgroup of order $m$ in $GL(n,q)$, ...

**15**

votes

**6**answers

1k views

### Fantastic properties of Z/2Z

Recently I gave a lecture to master's students about some nice properties of the group with two elements $\mathbb{Z}/2\mathbb{Z}$. Typically, I wanted to present simple, natural situations where the ...

**1**

vote

**2**answers

246 views

### When is PSU(2,q^2) = PSL(2,q) ?

The context for this question is from page 284 - 287 of Berger's paper: ...

**5**

votes

**3**answers

953 views

### Orthogonal Groups over finite fields

Hello
Let $\mathbb{F}_p$ be the finite field with $p$ elements. One can show that over finite fields, there are just two non-degenerate quadratic forms.
So here I want to pick
any non-degenerate ...

**4**

votes

**1**answer

274 views

### Aschbacher classes and $\mathbb{F}_p$-subspace stabilizers in classical linear groups

I am reading the Kleidman-Liebeck book ("The subgroup structure of the finite classical groups") which is about the Aschbacher classification of maximal subgroups of the classical almost simple ...

**10**

votes

**3**answers

916 views

### Can we always find such an irreducible polynomial of degree n where degree(p(x)-x^n)<= n/2?

Consider unitary polynomials of degree $n$ over $GF(2)$. That is, polynomials of the form $p(x) = \sum_{i=0}^n a_i x^i$ where $a_i\in GF(2)$ and $a_n=1$.
Can we always find such an irreducible ...

**5**

votes

**7**answers

531 views

### Classifications of finite simple objects

I'm curious to know if other classifications are known of "finite simple structures" in the same spirit of the monumental classification of finite simple groups. Here I mean "classification" in the ...

**4**

votes

**1**answer

1k views

### Order of finite unitary group

This may be an easy exercise but I am not getting it. Let $\mathbf F_q$ be a finite field with $q$ elements and $\mathbf F_{q^2}$ be its degree two extension. Define an automorphism $\sigma$ of ...

**17**

votes

**3**answers

850 views

### Non-split extensions of $GL_n(F_q)$ by $F_q^n$ ?

A very naive question :
I just learned that there is a non-split extension of $GL_3(F_2)$ by $F_2^3$ (with standard action). It can be realized as the subgroup of the automorphism group $G_2$ of ...

**3**

votes

**2**answers

899 views

### Cyclic order relation in Zn

The ring Zn:={0,1,..,n-1} under addition and multiplication modulo n.
Suppose a,b,c,x $\in$ Zn are nonzero and the cyclic order R(a,b,c) holds, then under what conditions does R(ax,bx,cx) hold ?

**23**

votes

**9**answers

2k views

### How many groups of size at most n are there? What is the asymptotic growth rate? And what of rings, fields, graphs, partial orders, etc.?

Question. How many (isomorphism types of) finite groups of size at most n are there? What is the asymptotic growth rate? And the same question for rings,
fields, graphs, partial orders, etc.
...