homological type
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2019 ◽  
Vol 29 (07) ◽  
pp. 1219-1234 ◽  
Author(s):  
Dessislava Kochloukova

We show that there are uncountably many non-commensurable metabelian pro-[Formula: see text] groups of homological type [Formula: see text] but not of type [Formula: see text], generated by [Formula: see text] element, where [Formula: see text] and [Formula: see text]. In particular there are uncountably many non-commensurable finitely presented metabelian pro-[Formula: see text] groups that are not of type [Formula: see text]. We show furthermore that there are uncountably many non-isomorphic one related 2-generated pro-[Formula: see text] groups.


2010 ◽  
Vol 151 (1) ◽  
pp. 323-359 ◽  
Author(s):  
Michele Rossi

2008 ◽  
Vol 11 (5) ◽  
Author(s):  
J. R. J. Groves ◽  
D. H. Kochloukova ◽  
C. F. Rodrigues

2006 ◽  
Vol 119 (1) ◽  
pp. 113-120 ◽  
Author(s):  
Ian James Leary ◽  
Müge Saadetoğlu
Keyword(s):  

2005 ◽  
Vol 72 (1) ◽  
pp. 109-127 ◽  
Author(s):  
Dessislava H. Kochloukova

We classify the Hopf algebras U (L)#kQ of homological type FP2 where L is a Lie algebra and Q an Abelian group such that L has an Abelian ideal A invariant under the Q-action via conjugation and U (L/A)#kQ is commutative. This generalises the classification of finitely presented metabelian Lie algebras given by J. Groves and R. Bryant.


2005 ◽  
Vol 15 (01) ◽  
pp. 175-205 ◽  
Author(s):  
STUART MCGLASHAN ◽  
ELTON PASKU ◽  
STEPHEN J. PRIDE

Monoids that can be presented by a finite complete rewriting system have both finite derivation type and finite homological type. This paper introduces a higher dimensional analogue of each of these invariants, and relates them to homological finiteness conditions.


2003 ◽  
Vol 13 (03) ◽  
pp. 341-359 ◽  
Author(s):  
Juan M. Alonso ◽  
Susan M. Hermiller

In 1987, Squier defined the notion of finite derivation type for a finitely presented monoid. To do this, he associated a 2-complex to the presentation. The monoid then has finite derivation type if, modulo the action of the free monoid ring, the 1-dimensional homotopy of this complex is finitely generated. Cremanns and Otto showed that finite derivation type implies the homological finiteness condition left FP3, and when the monoid is a group, these two properties are equivalent. In this paper we define a new version of finite derivation type, based on homological information, together with an extension of this finite derivation type to higher dimensions, and show connections to homological type FPnfor both monoids and groups.


2002 ◽  
Vol 12 (01n02) ◽  
pp. 247-284 ◽  
Author(s):  
YUJI KOBAYASHI ◽  
FRIEDRICH OTTO

For finitely presented monoids the homological finiteness conditions left-[Formula: see text], left-[Formula: see text], right-[Formula: see text] and right-[Formula: see text], the homotopical finiteness conditions of having finite derivation type [Formula: see text] and of being of finite homological type [Formula: see text] are developed and the relationship between these notions is investigated in detail. In particular, a result of Pride [40] and Guba and Sapir [27] on the exactness of a sequence of bimodules for the homotopy module is proved in a completely different, purely combinatorial manner. This proof is then translated into a proof of the corresponding result for the left homotopy module, thus giving new insights into the relationship between the finiteness conditions considered.


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