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pro vyhledávání: '"Kohl, Timothy"'
Autor:
Kohl, Timothy, Underwood, Robert
Let $K$ be a finite field extension of $\Q$ and let $N$ be a finite group with automorphism group $F=\Aut(N)$. R. Haggenm\"{u}ller and B. Pareigis have shown that there is a bijection \[\Theta: {\mathcal Gal}(K,F)\rightarrow {\mathcal Hopf}(K[N])\] f
Externí odkaz:
http://arxiv.org/abs/2010.05067
Autor:
Kohl, Timothy
For a group $G$, embedded in its group of permutations $B=Perm(G)$ via the left regular representation $\lambda:G\rightarrow B$, the normalizer of $\lambda(G)$ in $B$ is $\operatorname{Hol}(G)$, the holomorph of $G$. The set $\mathcal{H}(G)$ of those
Externí odkaz:
http://arxiv.org/abs/2005.10989
Autor:
Kohl, Timothy
The work of Greither and Pareigis details the enumeration of the Hopf-Galois structures (if any) on a given separable field extension. For an extension $L/K$ which is classically Galois with $G=Gal(L/K)$ the Hopf algebras in question are of the form
Externí odkaz:
http://arxiv.org/abs/1907.03844
Autor:
Kohl, Timothy
The Hopf-Galois structures on normal extensions $K/k$ with $G=Gal(K/k)$ are in one-to-one correspondence with the set of regular subgroups $N\leq B=Perm(G)$ that are normalized by the left regular representation $\lambda(G)\leq B$. Each such $N$ corr
Externí odkaz:
http://arxiv.org/abs/1806.06911
Let $ L/K $ be a finite separable extension of fields whose Galois closure $ E/K $ has group $ G $. Greither and Pareigis have used Galois descent to show that a Hopf algebra giving a Hopf-Galois structure on $ L/K $ has the form $ E[N]^{G} $ for som
Externí odkaz:
http://arxiv.org/abs/1711.05554
We discuss isomorphism questions concerning the Hopf algebras that yield Hopf-Galois structures for a fixed separable field extension $L/K$. We study in detail the case where $L/K$ is Galois with dihedral group $D_p$, $p\ge 3$ prime and give explicit
Externí odkaz:
http://arxiv.org/abs/1708.09822
Every Hopf-Galois structure on a finite Galois extension $K/k$ where $G=Gal(K/k)$ corresponds uniquely to a regular subgroup $N\leq B=\operatorname{Perm}(G)$, normalized by $\lambda(G)\leq B$, in accordance with a theorem of Greither and Pareigis. Th
Externí odkaz:
http://arxiv.org/abs/1708.08402
Autor:
Kohl, Timothy
For $p$ a prime and $a\in\mathbb{Q}$, where $a$ is not a $p^n$-th power of any rational number, the extension $\mathbb{Q}(w_n)/\mathbb{Q}$ where $w_n=\root p^n \of a$ is separable but non-normal. The Hopf-Galois theory for separable extensions was de
Externí odkaz:
http://arxiv.org/abs/1610.04630
Autor:
Kohl, Timothy
Publikováno v:
In Journal of Algebra 15 January 2020 542:93-115
Autor:
Kohl, Timothy
Publikováno v:
Algebra Number Theory 10 (2016) 37-59
For $\Gamma$ a group of order $mp$ for $p$ prime where $gcd(p,m)=1$, we consider those regular subgroups $N\leq Perm(\Gamma)$ normalized by $\lambda(\Gamma)$, the left regular representation of $\Gamma$. These subgroups are in one-to-one corresponden
Externí odkaz:
http://arxiv.org/abs/1405.4783