Autor(es)

Bridson, Martin R. ; Kochloukova, Dessislava H.

• Tipo de documento: Artigo Científico
• Fonte: COMMENTARII MATHEMATICI HELVETICI; v. 99, n. 1, p. 37-pg., 2024-01-01.

Resumo

The group AE(G) is obtained from G * G by forcing each element g in the first free factor to commute with the copy of g in the second free factor. We make significant additions to the list of properties that the functor AE is known to preserve. We also investigate the geometry and complexity of the word problem for AE(G). Subtle features of AE(G) are encoded in a normal abelian subgroup W < AE(G) that isa module over ZQ, where Q = H1(G, Z). We establish a structural result for this module and illustrate its utility by proving that AE preserves virtual nilpotence, the Engel condition, and growth type - polynomial, exponential, or intermediate. We also use it to establish isoperimetric inequalities for AE(G) when G lies in a class that includes Thompson's group F and all non-fibred K & auml;hler groups. The word problem is soluble in AE(G) if and only if it is soluble in G. The Dehn function of AE(G) is bounded below by a cubic polynomial if G maps onto a non-abelian free group. (AU)

• Processo FAPESP: 17/17320-9 - Propriedades combinatoriais, homológicas e geométricas de grupos
• Beneficiário: Dessislava Hristova Kochloukova
• Modalidade de apoio: Bolsas no Exterior - Pesquisa
• Processo FAPESP: 18/23690-6 - Estruturas, representações e aplicações de sistemas algébricos
• Beneficiário: Ivan Chestakov
• Modalidade de apoio: Auxílio à Pesquisa - Temático