4
votes
1answer
75 views

On group theory terminology

Let $G$ be a finite group. Consider the next number $$m(G):=\min\{m\in\mathbb{N}\mid G\ \text{can be embedded into}\ S_{m}\}.$$ It is obvious that Cayley's theorem yields $m(G)\leq |G|$. My ...
6
votes
1answer
59 views

Definition of $\Omega$-group and $\Omega$-composition series

What are the definitions of $\Omega$-group and $\Omega$-composition series? No luck searching on the internet..
1
vote
1answer
79 views

Why are regular $p$-groups called “regular?”

In the concept of regular $p$-Groups, what does "regularity" stand for? What is "regular" in such groups? I would like to know idea behind defining these groups, and naming these groups "regular." ...
6
votes
2answers
175 views

What is this method called - Abelization of a Group.

Today, I wanted to make a post for this question. There are some approach in which we can overcome the problem like this and this. According to my knowledge, I could solve the problem via the approach ...
1
vote
1answer
47 views

Use of the term “normal section” in a theorem of Maria Lucido.

Prop. 3 in this paper (p.135) states Let $G$ be a solvable group with $\text{diam}\Gamma(G)=4$. Then either $l_F(G)\leq 3$ or $l_F(G)=4$ and $G$ has a normal section isomorphic to $H$. ($H$ is ...
9
votes
0answers
142 views

Official name(s) for a certain type of p-group

I'm implementing a class of groups into Sage (sagemath.org), a computer algebra system, and I'm wondering if it has any official names. I found it in Gorenstein's "Finite Groups." It is there called ...
1
vote
0answers
70 views

What could the meaning of “invariant of $G$” be?

In a context, the author wrote that for a finite permutation group $G$ acting on a set $\Omega$ of degree $n$, the list of subdegrees is an invariant of the group. What could the meaning of ...
3
votes
0answers
133 views

Terminology in Dickson's book

This appears in Dickson's "Linear Groups with an exposition of the Galois field theory", page 50, chapter 4. My question is: how would the above "translate" in modern terms? In particular, do we ...