Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: FPn properties of generalized Houghton groups   This Thesis presents a 2-dimensional generalization of Houghtons' groups H_n.
H_n is defined to be the group of all permutations p of a disjoint union of
copies of the natural numbers N, with the property that each copy of N contains
a cofinite subset on which p restricts to a translation. Our group G(n) is
defined to be the group of all permutations p of a disjoint union of quadrants
(i.e., copies of NxN) with the property that each quadrant contains a
subquadrant on which p is a translation, while p restricted to the remaining
set is piecewise isometric on a cofinite disjoint union of rays (each isometric
to N). Based on K.S. Brown's treatment of the Houghton group case it is shown
that G(n) is of type FP(n-1); in fact, that G(n) contains a normal subgroup N
with G(n)/N = Z^(n-1) which is of type FP(n-1) and not FPn.

23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg