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Keywords:
infinite simple group; HNN extension; nearring with identity
infinite simple group; HNN extension; nearring with identity
Summary:
We investigate conditions on an infinite simple group in order to construct a zero-symmetric nearring with identity on it. Using the Higman-Neumann-Neumann extensions and Clay's characterization, we obtain zero-symmetric nearrings with identity with the additive groups infinite simple groups. We also show that no zero-symmetric nearring with identity can have the symmetric group ${\rm Sym}(\mathbb {N})$ as its additive group.
References:
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