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profinite group is a topological group that is in a certain sense assembled from a system of finite groups. The idea of using a profinite group is to provide...

closed subgroups of finite index, so that the discrete quotient group is always finite. Alternatively, one can define a pro-p group to be the inverse limit...

where the finite groups Z / p n {\displaystyle \mathbb {Z} /p^{n}} are given the discrete topology. Another large class of pro-finite groups important...

linear group Group of Lie type Group scheme HN group Janko group Lie group Simple Lie group Linear algebraic group List of finite simple groups Mathieu...

of finite p-groups via the coclass conjectures (Leedham-Green & McKay 2002), and provided an excellent method of understanding analytic pro-p-groups (Dixon...

G. Every finite p-group is nilpotent. The remainder of this article deals with finite p-groups. For an example of an infinite abelian p-group, see Prüfer...

(category theory) Pullback (category theory)/fiber product Inverse limit Pro-finite group Colimit Coproduct Coequalizer Cokernel Pushout (category theory) Direct...

R[t]/t^{n}R[t]} given by the natural projection. Pro-finite groups are defined as inverse limits of (discrete) finite groups. Let the index set I of an inverse system...

to the cohomology of the group G (for (pro-)finite groups G). From it, one gets the inflation-restriction exact sequence. Group cohomology is closely related...

the same period when the fundamental group was generalised to the algebraic geometry setting (as a pro-finite group). In the light of later work (c. 1970)...

that the fundamental group is exactly the group of deck transformations of the universal covering space. This is more promising: finite étale morphisms of...

component of G is pro-reductive. The groups of Lie type are the finite simple groups constructed from simple algebraic groups over finite fields. Lang's...

between finite and non-finite clauses. A finite clause contains a structurally central finite verb, whereas the structurally central word of a non-finite clause...

Institute for Advanced Study in Princeton a year long program on "Pro-finite groups and the congruence subgroup problem". In 2006, he got an honorary...

mathematical notions. If C is the category of finite groups, then pro-C is equivalent to the category of profinite groups and continuous homomorphisms between...

group theory, a descendant tree is a hierarchical structure that visualizes parent-descendant relations between isomorphism classes of finite groups of...

by group theorists including D. Johnson (1988) and the name "Nottingham group" refers to his former domicile. This group is a finitely generated pro-p-group...

pro-finite if each term of the inverse system of simplicial sets has finite homotopy groups. Pro-simplicial sets show up in shape theory, in the study of localization...

quasi-finite fundamental group scheme π qf ( X , x ) {\displaystyle \pi ^{\text{qf}}(X,x)} if there exist a pro-quasi-finite and flat π qf ( X , x ) {\displaystyle...

group of a concrete, pro-finite group which respects certain structures that are essential to this group." This fundamental, Galois group theory in mathematics...