Combinatorial Group Theory

By Charles F. Miller. 2002

2,415 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/3310e7c5b51e65bf5a308a5c8930bc99702ee766

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Citations in the corpus

Transitivity degrees of countable groups and acylindrical hyperbolicity (2015, background): “Neumann (see [36]); finitely generated examples can be found in [51].”
Simplicial nonpositive curvature (2006, background): “These constitute a significant part of small cancellation theory [LS], which deals mostly with 2-dimensional complexes.”
Cohomological goodness and the profinite completion of Bianchi groups (2008, background): “4 in [16] any subgroup of finite index of a F-group is again a F-group and so a torsion free subgroup of a F-group of finite index is a finitely generated free group or a surface group.”
Endomorphic presentations of branch groups (2000, background): “images of all φ∈ Φ, and adds φ(s) to R. 2.1. Embeddings. We start by some motivation for the study of L-presentations. Recall Graham Higman’s Embedding Theorem Theorem 2.3 ([Hig61] or Section IV.7 of [LS70]). A countable group G can be embedded in a ﬁnitely presented group Gb if and only if it is re”
Conjugacy in Garside groups III: Periodic braids (2006, unknown): “3 of [26]) to decompose X as a product of elements in Pn,2.”
Basis-conjugating automorphisms of a free group and associated Lie algebras (2006, background): “It follows from [17] that Aut(Fn) is generated by the elements • ξi for 1 ≤ i ≤ n, • τi for 1 ≤ i ≤ n and • δ .”
Weakly Modular Graphs and Nonpositive Curvature (2014, background): “of Dis a plane graph whose inner faces are exactly the 2{cells of Dand there exists a cellular map ’: D!X such that ’j@D = C (for more details see [LS01, Chapter V]). According to Van Kampen’s lemma ([LS01], pp. 150{151), for every cycle Cof a simply connected simplicial complex, one can construct a”
Free holomorphic automorphisms of the unit ball of B(ℋ) n (2008, background): “We prove in [27] that the Hausdorff derivations ([14]) ∂ ∂Zi , i = 1, .”
Orbit decidability and the conjugacy problem for some extensions of groups (2007, methodology): “By Higman’s embedding theorem (see [25]), B embeds in a finitely presented group B′ 6= 1, which then embeds inG1 = B′∗Z.”
Small cancellation in acylindrically hyperbolic groups (2013, background): “In the case where gn+1 has order k, it is well-known that the order of vn+1 in J is k (see [21]).”
Normal subgroups in the Cremona group (2010, background): “Recall that this lemma claims the existence of a region with a large external segment in a van Kampen diagram (see [44], Chapter V).”
Combinatorial algebra : syntax and semantics (2014, unknown): “Indeed (see [210]) every HNN extension is a subgroup of some natural free product with amalgamation, and every free product with amalgamation is inside some natural HNN extension.”