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Everything about Profinite group
Topological group that is in a certain sense assembled from a system of finite groups
In mathematics, a profinite group is a topological group that is in a certain sense assembled from a system of finite groups. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Profinite groupA 5-minute orientation
- Skim a recent paper: The pro-norm of a profinite groupInfluential work since 2022
- Pick up a classic book: Lectures on profinite topics in group theoryThe most-reprinted book on the subject
- Read the landmark paper: On The Profinite Topology on a Free GroupCited 91 times
- Go sideways: Grothendieck's Galois theoryA closely related topic
- Go sideways: Profinite integerA closely related topic
📖 Definitions
Noun A topological group that is isomorphic to the inverse limit of some inverse system of discrete finite groups; equivalently, a topological group that is also a Stone space.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
On The Profinite Topology on a Free Group
Random generation of finite and profinite groups and group enumeration
Profinite completion of operads and the Grothendieck–Teichmüller group
Mapping-class-group action versus Galois action on profinite fundamental groups
Monoid kernels and profinite topologies on the free Abelian group
Continuous group actions on profinite spaces
Inverse automata and profinite topologies on a free group
Small profinite groups
🆕 Influential since 2022
📚 Books worth reading
Lectures on profinite topics in group theoryBenjamin Klopsch · 2011
Profinite groupsLuis Ribes, Pavel Zalesskii · 2000- 📕Grupos profinitos, grupos libres y productos libresLuis Ribes · 1977
- 📕Deformation theory of Galois representationsNigel Boston · 1987
Profinite groupsWilson, John S. · 1998
WordsDaniel Segal · 2009
Linear pro-p-groups of finite widthG. Klaas · 1997
Profinite groupsLuis Ribes · 2010
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Grothendieck's Galois theory In mathematics, Grothendieck's Galois theory is an abstract approach to the Galois theory of fields, developed around 1960 to provide a way to study the…
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- Field arithmetic In mathematics, field arithmetic is a subject that studies the interrelations between arithmetic properties of a field and its absolute Galois group. It…
- Class formation In mathematics, a class formation is a topological group acting on a module satisfying certain conditions. Class formations were introduced by Emil Artin…
- Embedding problem In Galois theory, a branch of mathematics, the embedding problem is a generalization of the inverse Galois problem. Roughly speaking, it asks whether a…
- Topological group In mathematics, topological groups are groups and topological spaces at the same time, where the group operations are required to be continuous. This connects…
- Galois group In Galois theory, a branch of abstract algebra, the Galois group of a certain type of field extension is a symmetry group characterizing how it extends…
- Residually finite group In the mathematical field of group theory, a group G is residually finite or finitely approximable if for every element g that is not the identity in G…