Tagged Questions

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

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How to get state space equation for given matrix

state space equations (any realization) How to write state space equation for this matrix having two transfer function on it. [(s2 + 1)/(s2 + 5s + 6) (s + 2)/(s + 3)] I also need to check this ...
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1answer
367 views

Is there any simple proof for this?

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. ...
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39 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 ...
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1answer
65 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 ...
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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 ...
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1answer
53 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 ...
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1answer
158 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 ...
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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 ...
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318 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
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1answer
476 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. ...
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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 ...
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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, $P \in \operatorname{Syl}_p(G)$ ...