For questions about the transfer homomorphism in group theory and its applications.

learn more… | top users | synonyms

0
votes
1answer
27 views

MATLAB Feedback

I am trying to use the feedback function in matlab and for the most part I understand it. But I came across this syntax: [x1 x2] = feedback(sys1, sys2, 1, 1, -1); ...
23
votes
1answer
470 views

Showing that $ϕ(x)=x^n$ is a homomorphism from $G\to Z(G)$

Let $G$ be a group with $|G:Z(G)|=n$ then $\phi(x)=x^n$ is a homomorphism from $G$ to $Z(G)$. I guess it has a proof using transfer theory, I wonder whether it has an elemantary proof or not. ...
0
votes
1answer
43 views

Manually trying to calculate output of an transfer function.

I am trying to calculate the output of an transfer function due to the input of an step, But some weird reason, I am only getting the inverse output, what Matlab says it should be. My transfer ...
1
vote
1answer
68 views

Schur's Theorem about the derived subgroup

(Schur) Suppose Z(G) is of finite index in G, then the derived subgroup of G is finite. We know Schur's lemma that says: Let |G:Z(G)|=m. Then the map g to g^m is a homomorphism from G into ...
0
votes
1answer
73 views

Schur's theorem in transfer theory

M.Isaacs’ Algebra a graduate course page 119 : (Schur). Let $|G:Z(G)|=m<∞$. Then the map $g↦g^m$ is a homomorphism from G into Z(G). Proof. In fact, we will show that this map is the transfer ...
1
vote
1answer
55 views

transfer evaluation lemma

Let $M$ normal in $H\subseteq G$ with $[G:H]<\infty$ and $H/M$ abelian, and let $T$ be a right transversal for $H$ in $G$, there exists a subset $T_0\subseteq T$ and positive integers $n_t$ for ...
0
votes
1answer
170 views

Analyse closed loop transfer function

I have a transfer function from $x_c$ to $x$ $ \dfrac{x_c}{x} = \dfrac{k}{s + k} $ And I want to analyse the stability and find the best possible value for k. I've tried to convert the closed loop ...
4
votes
0answers
100 views

What is the relationship between solvable, nilpotent and transfer homomorphism?

I know some facts such as: Nilpotent groups are solvable, $p$-groups are nilpotent, a finite group whose order is a product of distinct primes is solvable, and finite groups are nilpotent if and only ...
8
votes
1answer
337 views

An Intuitive Explanation of the Transfer Homomorphism

I just learned about the transfer homomorphism, and I am having trouble internalizing it. I am learning from 'A Course in the Theory of Groups', and I was hoping that perhaps someone had a more ...
6
votes
1answer
517 views

What is the relationship between Mackey's theorem in character theory and Mackey's theorem in transfer theory?

Here are the statements of the two theorems. The first statement I took from a paper I have been reading, but I believe can also be found in Isaacs' Character Theory of Finite Groups as an exercise. ...
4
votes
0answers
172 views

Easy proof of trivial fusion implies normal p-complement

Theorem: Suppose G is a finite group with Sylow p-subgroup P. Then the following are equivalent: The set K of elements of G of order relatively prime to p (the p′-elements) form a subgroup If A and ...
7
votes
0answers
193 views

A problem in transfer theory

This is about problem 5B.1 page 157 in Isaacs' "Finite Group Theory" book. This chapter is definitely giving me trouble. The problem reads: Let $G$ be a finite group, $P \in \operatorname{Syl}_p(G)$ ...