Skip to main content
We gratefully acknowledge support from the Simons Foundation, member institutions, and all contributors. Donate
arXiv logo
Cornell University Logo

Mathematics > Group Theory

arXiv:1805.10830 (math)
[Submitted on 28 May 2018 (v1), last revised 15 Sep 2018 (this version, v2)]

Title:Non-existence of Hopf-Galois structures and bijective crossed homomorphisms

Authors:Cindy Tsang
View PDF
Abstract:By work of C. Greither and B. Pareigis as well as N. P. Byott, the enumeration of Hopf-Galois structures on a Galois extension of fields with Galois group $G$ may be reduced to that of regular subgroups of $\mbox{Hol}(N)$ isomorphic to $G$ as $N$ ranges over all groups of order $|G|$, where $\mbox{Hol}(-)$ denotes the holomorph. In this paper, we shall give a description of such subgroups of $\mbox{Hol}(N)$ in terms of bijective crossed homomorphisms $G\longrightarrow N$, and then use it to study two questions related to non-existence of Hopf-Galois structures.
Comments: Accepted version
Subjects: Group Theory (math.GR); Number Theory (math.NT)
Cite as: arXiv:1805.10830 [math.GR]
  (or arXiv:1805.10830v2 [math.GR] for this version)
  https://doi.org/10.48550/arXiv.1805.10830
Journal reference: J. Pure Appl. Algebra 223 (2019), no. 7, 2804-2821
Related DOI: https://doi.org/10.1016/j.jpaa.2018.09.016

Submission history

From: Cindy (Sin Yi) Tsang [view email]
[v1] Mon, 28 May 2018 09:16:31 UTC (17 KB)
[v2] Sat, 15 Sep 2018 05:58:09 UTC (17 KB)
Full-text links:

Access Paper:

view license
Current browse context:
math.GR
< prev   |   next >
new | recent | 2018-05
Change to browse by:
math
math.NT

References & Citations

export BibTeX citation

Bookmark

BibSonomy logo Reddit logo

Bibliographic and Citation Tools

Bibliographic Explorer (What is the Explorer?)
Connected Papers (What is Connected Papers?)
Litmaps (What is Litmaps?)
scite Smart Citations (What are Smart Citations?)

Code, Data and Media Associated with this Article

alphaXiv (What is alphaXiv?)
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub (What is DagsHub?)
Gotit.pub (What is GotitPub?)
Hugging Face (What is Huggingface?)
Papers with Code (What is Papers with Code?)
ScienceCast (What is ScienceCast?)

Demos

Replicate (What is Replicate?)
Hugging Face Spaces (What is Spaces?)
TXYZ.AI (What is TXYZ.AI?)

Recommenders and Search Tools

Influence Flower (What are Influence Flowers?)
CORE Recommender (What is CORE?)

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)