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On zero-symmetric nearrings with identity whose additive groups are simple

Wen-Fong Ke, Johannes H. Meyer, Günter F. Pilz, Gerhard Wendt (2024)

Czechoslovak Mathematical Journal

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 Sym ( ) as its additive group.

Opérades cellulaires et espaces de lacets itérés

Clemens Berger (1996)

Annales de l'institut Fourier

L’espace des configurations de p points distincts de R admet une filtration naturelle qui est induite par les inclusions des R n dans R . Nous caractérisons le type d’homotopie de cette filtration par les propriétés combinatoires d’une structure cellulaire sous-jacente, étroitement liée à la théorie des E n -opérades de May. Cela donne une approche unifiée des différents modèles combinatoires d’espaces de lacets itérés et redémontre les théorèmes d’approximation de Milgram, Smith et Kashiwabara.

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