In mathematics, the HNN extension is an important construction of combinatorial group theory. Introduced in a 1949 paper Embedding Theorems for Groups...

applications of the operations of free product with amalgamation and HNN extension, via the notion of the fundamental group of a graph of groups. Bass–Serre...

HNN may refer to: HLN (TV channel), an American television news channel HNN extension, in combinatorial group theory Hanunó'o language, spoken in the...

mechanics. Lie algebra extension Virasoro algebra HNN extension Group contraction Extension of a topological group group+extension#Definition at the nLab...

polynomial time. The Baumslag–Gersten group G can also be realized as an HNN extension of the Baumslag–Solitar group B S ( 1 , 2 ) = ⟨ a , b ∣ a b = a 2 ⟩...

constructed from finite groups using amalgamated free products and HNN extensions. Using the action of the modular group on a certain tessellation of...

Section 5 of Chapter IV of Lyndon and Schupp for the Moldavansky's HNN-extension version of that approach. Let G be a one-relator group given by presentation...

normal form theorems for a free product with amalgamation and for an HNN extension (Bass 1993). Let Γ be the fundamental group corresponding to the spanning...

Scholarship, Wrong Conclusions". HNN Special: A Symposium on Jonah Goldberg's Liberal Fascism. George Mason University (HNN). Archived from the original on...

for a knot K, then the fundamental group of S3 − N(K) splits as an HNN extension over π1(S), which is a free group. The two maps from π1(S) into π1(S3...

generalized for describing subgroups of amalgamated free products and HNN extensions. Other generalizations include considering subgroups of free pro-finite...

Higman's embedding theorem Feit-Higman theorem Higman group Higman's lemma HNN extension Hall–Higman theorem Conder, Marston D. E. (2022). "Graham Higman. 19...

admits a nontrivial splitting as an amalgamated free product or as an HNN extension over a finite group (that is, in terms of Bass–Serre theory, if and...

one-ended groups via a finite number of amalgamated free products and HNN extensions over finite subgroups. In view of the Stallings theorem about ends of...

admits a nontrivial decomposition as an amalgamated free product or an HNN extension over a finite subgroup. In the modern language of Bass–Serre theory...

Schreier's method, Nielsen's method, free presentations, subgroups and HNN extensions, Golod–Shafarevich theorem, etc. Sims, Charles C. (1994). Computation...

graph. Every right-angled Artin group of rank r can be constructed as HNN extension of a right-angled Artin group of rank r − 1 {\displaystyle r-1} , with...

celebrating women's achievements in mathematics. Hanna Neumann conjecture HNN extension February 12#Births Fowler, Kenneth F. "Neumann, Hanna (1914–1971)"....

only if it is either a nontrivial free product with amalgamation or HNN-extension with finite amalgamation. All other finitely generated infinite groups...

Novikov–Boone theorem via a clever use of amalgamated products and HNN extensions. Let P {\displaystyle P} be a Markov property and let A + , A − {\displaystyle...

has property FA, then it cannot split as an amalgamated product or HNN extension; indeed, if G is contained in an amalgamated product then it is contained...

admits an essential splitting, as an amalgamated free product or an HNN extension, over a virtually infinite cyclic group. This allowed Bowditch to produce...

practice. The algorithm is shown to be in GenL. The conjugacy problem in HNN extensions can be unsolvable even for free groups. However, it is generically cubic...

amalgamated free product G = A ∗ C B {\displaystyle G=A\ast _{C}B} or an HNN-extension G = A ∗ C {\displaystyle G=A\ast _{C}} where C is a finite group. Then...

prize named in his honour. The group-theoretic notion of HNN (Higman-Neumann-Neumann) extension bears the names of Bernard and his wife Hanna, from their...

version of small cancellation theory for amalgamated free products and HNN-extensions. Small cancellation theory was further generalized by Alexander Ol'shanskii...

problem as well. The usual proof of the theorem uses a sequence of HNN extensions starting with R and ending with a group G which can be shown to have...

fundamental groups of such bundles give an important class of HNN-extensions: that is, extensions of the fundamental group of the fiber (a surface) by the...

with respect to a collection of proper subgroups is SQ-universal. Many HNN extensions, free products and free products with amalgamation. The four-generator...

produce not just free products but also amalgamated free products and HNN extensions. These generalizations are used, in particular, in the proof of Maskit's...