Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Small cancellation theory over Burnside groups   We develop a version of small cancellation theory in the variety of Burnside
groups. More precisely, we show that there exists a critical exponent $n_0$
such that for every odd integer $n\geq n_0$, the well-known classical
$C'(1/6)$-small cancellation theory, as well as its graphical generalization
and its version for free products, produce examples of infinite $n$-periodic
groups. Our result gives a powerful tool for producing (uncountable collections
of) examples of $n$-periodic groups with prescribed properties. It can be
applied without any prior knowledge in the subject of $n$-periodic groups.
  As applications, we show the undecidability of Markov properties in classes
of $n$-periodic groups, we produce $n$-periodic groups whose Cayley graph
contains an embedded expander graphs, and we give an $n$-periodic version of
the Rips construction. We also obtain simpler proofs of some known results like
the existence of uncountably many finitely generated $n$-periodic groups and
the SQ-universality (in the class of $n$-periodic groups) of free Burnside
groups.

19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con
23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th