On semigroup presentations that define a group
Tóm tắt
We consider the finite semigroup presentations of the form
$$\begin{aligned} \mathcal {P}=\langle a_1,\cdots ,a_n\mid w_1=a_1,\cdots ,w_n=a_n \rangle \end{aligned}$$
and their Adian graphs. It is known that if both Adian graphs of
$$\mathcal {P}$$
are connected and if one of the Adian graphs of
$$\mathcal {P}$$
is a cycle graph then
$$\mathcal {P}$$
defines a group (see 2008). We extend this result to certain presentations such that neither of the Adian graphs are cycle graphs.
Tài liệu tham khảo
Ayık, G., Ayık, H., Ünlü, Y.: On semigroup presentations and Adian graphs. Discrete Math. 308(11), 2288–2291 (2008)
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Ayık, H., Kuyucu, F., Vatansever, B.: On semigroup presentations and efficiency. Semigroup Forum 63, 231–242 (2002)
Campbell, C.M., Mitchell, J.D., Ruškuc, N.: On defining groups efficiently without using Inverses. Math. Proc. Cambridge Philos. Soc 133, 31–36 (2002)
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