On the width in free products with amalgamation

Verbal subgroups of hyperbolic groups have infinite width

“…from (2), so the paths ι(p ) and p 0 in K, corresponding to the group element g 0 , asynchronously H 0 -fellow travel, where H 0 ultimately depends only on the presentation of the group G and the word w. Choosing H = 2H 0 in the definition of ∆ ω (see ( 4) and ( 5)), by Lemma 6 we may choose M large enough so that ∆ ω (p 0 ) = ∆ ω (p ). Taking (9) into account, we conclude γ(g 0 ) ≤ 72r + 72.…”

“…Bardakov showed that HNN extensions with proper associated subgroups and one-relator groups with at least three generators are verbally parabolic [1]; as well as braid groups B n [2]. For amalgamated free products Dobrynina improved on the previous partial results by showing that A * U B is verbally parabolic, provided U = A and U bU = U b −1 U for some b ∈ B [9].…”

On the palindromic and primitive widths of a free group

“…We can mention results on the width of matrix groups with respect to the set of transvections (see, e.g., [1,4,20]) and the study of the width of verbal subgroups of various free constructions [2,7,8,15,17].…”

Mass and width of strange baryon resonances using QCD sum rules

“…Some of these width variants include verbal width, palindromic width, and C-width. For a comprehensive overview of results related to these different width concepts, readers can refer to the following references: [11,4,2,1,3,6,7,5,9,10,12,14]. We will focus on C-width of some free constructions of groups.…”