Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A mixed identity-free elementary amenable group   A group $G$ is called mixed identity-free if for every $n \in \mathbb{N}$ and
every $w \in G \ast F_n$ there exists a homomorphism $\varphi: G \ast F_n
\rightarrow G$ such that $\varphi$ is the identity on $G$ and $\varphi(w)$ is
nontrivial. In this paper, we make a modification to the construction of
elementary amenable lacunary hyperbolic groups given by Ol'shanskii, Osin, and
Sapir to produce finitely generated elementary amenable groups which are mixed
identity-free. As a byproduct of this construction, we also obtain locally
finite $p$-groups which are mixed identity-free.

13
The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
27
The categories of this paper are: comp-gas
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
19
The categories of this paper are: eess
24
The categories of this paper are: dg-ga
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
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The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci