Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Natural dualities, nilpotence and projective planes   We use an interpretation of projective planes to show the inherent
nondualisability of some finite semigroups. The method is sufficiently flexible
to demonstrate the nondualisability of (asymptotically) almost all finite
semigroups as well as to give a fresh proof of the Quackenbush-Szab\'o result
that any finite group with a nonabelian Sylow subgroup is nondualisable. A
novel feature is that the ostensibly different notions of nilpotence for
semigroups, nilpotence for groups, and the property of being nonorthodox for a
completely 0-simple semigroup are unified by way of a single construction. We
also give a semigroup example of two dualisable finite semigroups whose direct
product is inherently nondualisable.

20
The categories of this paper are: acc-phys
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
26
The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
14
The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics