Questions tagged [frobenius-groups]
Use this tag for questions about Frobenius groups, kernels and complements.
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The lower bound of Frobenius norm of matrices product.
Let $A,B \in M_p(R)$ be symmetric matrices, $A$ is given and non-singular, where $\|.\|$ is Frobenius norm.
I would like to find the lower bound of $\|A^{-1}.B.(A+B)^{-1}\|$:
I have the result:
$$\|A^{...
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About Frobenius Groups of order 1029
In the list of groups in GAP of order $1029=7^3\cdot 3$, there are two, with structure description $U_3(\mathbb{F}_7)\rtimes C_3$.
(Among $19$ groups $G[1], G[2], \ldots, G[19]$ of order $1029$, the ...
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Frobenius algebra structure over complex polynomials modulo $x^2$.
I was trying to define a Frobenius Algebra structure over complex polynomials modulo $x^2$, but I am really struggling to do so.
The algebra structure is rather evident, but I've tried many possible ...
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$G$ a group with center $\{e\}$ and $A$ a maximal subgroup of $G$ that is also abelian and not normal. How to show that $A$ is a Frobenius complement?
I have been sitting on this homework problem for days now:
As the title says, I have a group (which doesn't have to be finite. Even Frobenius groups aren't defined as finite in our course) which only ...
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Subgroup containing normalizers of its $p$-subgroups
This is exercise $1.D.5$ of Isaacs' "Finite Group Theory". It goes:
Let $G$ be a finite group and let $H$ be a subgroup of $G$. Suppose $N_G(P) \subset H$ for all $p$-subgroups $1 \neq P$ ...
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If $G$ is nonabelian & solvable s.t. the centralizer of each nontrivial element is abelian, then $G$ is Frobenius with kernel its Fitting subgroup
I'm dealing with the following problem in Isaacs Finite Group Theory [6A.5], I would appreciate if you could help:
Let $G$ be a nonabelian solvable group in which the centralizer of every nonidentity ...
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Determine the order of the Frobenius automorphism
If $\Phi(x)=x^{p}$ is the Frobenius automorphism of $\mathbb{F}_{q}$, where $q = p^d$ , what is the smallest integer $\alpha$ such that $\Phi^{\alpha}=\text{Id}$?
Since the order of the group $\mathbb{...
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On the Frobenius group
I am studying some properties of Frobenius group $G$ of order $20$, which mean that a presentation of the group $G$ is
$$G = \langle c, f \mid c^5 = f^4 = 1, \,cf = fc^2\rangle.$$
My question is ...
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Explanation of Frobenius endomorphism on elliptic curves
I'm trying to understand how to calculate the Frobenius endomorphism for an elliptic curve.
Specifically, If $E$ is defined over $\mathbb{F}_q$, then the Frobenius endomorphism $\pi$ is defined as
$\...
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$y$ centralizes $fzf^{-1} $ for some $f \in F(G)$.
Let $G$ be a finite and soluble group with a trivial center. We assume that $C_G(x_r)$ acts free of fixed points on $F(G)$ by conjugation and $C_G(x_r)F(G)$ is a Frobenius group with complement $C_G(...
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I want to show that $G=C_G(z)F(G)$
Let $G$ be a finite and soluble group with a trivial center. We assume that $C_G(x_r)$ acts free of fixed points on $F(G)$ by conjugation and $C_G(x_r)F(G)$ is a Frobenius group with complement $C_G(...
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Subgroups of Frobenius group
Let $G=N\rtimes M$ be a finite Frobenius group with kernel $N$ and complement $M$. Suppose that $N$ is a minimal normal subgroup of $G$, while $M$ is maximal in $G$. Is there a result which states ...
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Frobenius Problem
Let a[1],...,a[n] be positive integer such that gcd(a[1],...,a[n])=1 and a[1]<...< a[n]
how can find number such that "Max number of representable is 1 in linear combination" for example :
a[...
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What reference books or papers address Frobenius groups: in particular, of order (121)(120)?
I have constructed (as a permutation group on 121 points) a Frobenius group of order (121)(120) with kernel K = $C_{11}^2$ and cyclic complement H of order 120. I have checked its properties very ...
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A question about Frobenius action
On page 177 of my textbook Finite Group Theory by I. Martin Isaacs, it says:
Let $A$ and $N$ be finite groups, and suppose that $A$ acts on $N$ via automorphisms. The action of $A$ on $N$ is said ...
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