Geodesic
On the word problem for the free Burnside semigroups satisfying~$x^2=x^3$
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2011), pp. 89-93

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We study the word problem for free Burnside semigroups satisfying the identity $x^2=x^3$. For any $k>2$ we prove that the word problem for the $k$-generated free Burnside semigroup $B(2,1,k)$ can be reduced to the word problem for the two-generated semigroup $B(2,1,2)$. Moreover, if every element of $B(2,1,2)$ is a regular language, then every element of $B(2,1,k)$ also appears to be a regular language. Therefore, the semigroup $B(2,1,k)$ satisfies the Brzozowski conjecture if and only if so does $B(2,1,2)$.
Keywords: free Burnside semigroups, word problem, Brzozowski conjecture. 
@article{IVM_2011_11_a10,
     author = {A. N. Plyushchenko},
     title = {On the word problem for the free {Burnside} semigroups satisfying~$x^2=x^3$},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {89--93},
     publisher = {mathdoc},
     number = {11},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2011_11_a10/}
}
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A. N. Plyushchenko. On the word problem for the free Burnside semigroups satisfying~$x^2=x^3$. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2011), pp. 89-93. http://geodesic.mathdoc.fr/item/IVM_2011_11_a10/