Geodesic
On zero-symmetric nearrings with identity whose additive groups are simple
Czechoslovak Mathematical Journal, Tome 74 (2024) no. 3, pp. 869-880 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
DOI : 10.21136/CMJ.2024.0086-24
Classification : 16Y30, 20B30, 20E06, 20E32
Keywords: infinite simple group; HNN extension; nearring with identity 
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     title = {On zero-symmetric nearrings with identity whose additive groups are simple},
     journal = {Czechoslovak Mathematical Journal},
     pages = {869--880},
     year = {2024},
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Ke, Wen-Fong; Meyer, Johannes H.; Pilz, Günter F.; Wendt, Gerhard. On zero-symmetric nearrings with identity whose additive groups are simple. Czechoslovak Mathematical Journal, Tome 74 (2024) no. 3, pp. 869-880. doi: 10.21136/CMJ.2024.0086-24

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