Normal subsets of quasigroups
Let be a loop. If is such that for each standard generator of Inn, then does not have to be a normal subloop. In an LC loop the left and middle nucleus coincide and form a normal subloop. The identities of Osborn loops are obtained by applying the idea of nuclear identification, and various connections of Osborn loops to Moufang and CC loops are discussed. Every Osborn loop possesses a normal nucleus, and this nucleus coincides with the left, the right and the middle nucleus. Loops that...
Let be a field, G a reductive algebraic -group, and G 1 ≤ G a reductive subgroup. For G 1 ≤ G, the corresponding groups of -points, we study the normalizer N = N G(G 1). In particular, for a standard embedding of the odd orthogonal group G 1 = SO(m, ) in G = SL(m, ) we have N ≅ G 1 ⋊ µm(), the semidirect product of G 1 by the group of m-th roots of unity in . The normalizers of the even orthogonal and symplectic subgroup of SL(2n, ) were computed in [Širola B., Normalizers and self-normalizing...
In questo lavoro si studiano i gruppi finiti di ordine una potenza di un numero primo in cui i sottogruppi normali sono compresi tra due termini successivi della serie centrale discendente. Si ottengono numerose proprietà generali di questi gruppi, e una loro dettagliata descrizione in classe di nilpotenza 2.
On classifie les orbites de sur l’immeuble de Bruhat-Tits de pour trois paires sphériques de groupes -adiques classiques.