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

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Problems in understanding a passage in the proof of Grün theorem for transfer

This is the statement of the theorem: Let $P$ a Sylow $p$-subgroup of $G$ and $Z$ a subgroup of $Z(P)$ that is weakly closed in $P$. Set $H=N_G(Z)$. Then $P\cap G'=P\cap H'$ and $P/(P\cap G')\simeq ...
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Transfer function for series RLC-filter

I am stuck trying to convert a transfer function of a series RLC-filter to standard form so that I can determine L and C at a given frequency. (R is known). The filter is L in series and R+C in ...
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Transfer homomorphism: is this proof correct?

I'm doing a guided exercise to learn the transfer homomorphism. The preliminaries are these: Given a finite group $G$ and a subgroup $H<G$, let $\{ x_iH \}_{i\in I}$ be the set of left cosets of ...
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On the Transfer Homomorphism

I'm approaching the study of the transfer homomorphism between groups, and I found this exercise: Given a finite group $G$ and a subgroup $H<G$, the set of left cosets of $H$ in $G$ is written $ ...
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How do I determine the transfer function of a plant?

I sitting here with a system which I have to determine the transfer function. The unit receives a velocity and position, and move towards that position with the given velocity. What kind of test ...
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Condition Butterworth polynomial

My course states that a polynomial is a Butterworth polynomial when it satisfies the following condition: $|B(j\Omega)|=\sqrt {1+{\Omega}^{2\,n}}=\sqrt {1+{(\omega/\omega_p)}^{2\,n}}$ I'm really ...
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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); ...
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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. ...
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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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105 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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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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294 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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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 ...
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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 ...