We prove a natural generalization of Szep’s conjecture. Given an almost simple group G with socle not isomorphic to an orthogonal group having Witt defect zero, we classify all possible group elements x, y∈ G\ { 1 } with G= NG(⟨ x⟩) NG(⟨ y⟩) , where we are denoting by NG(⟨ x⟩) and by NG(⟨ y⟩) the normalizers of the cyclic subgroups ⟨ x⟩ and ⟨ y⟩ . As a consequence of this result, we classify all possible group elements x, y∈ G\ { 1 } with G= CG(x) CG(y) .
Gill, N., Giudici, M., Spiga, P. (2023). A Generalization of Szep’s Conjecture for Almost Simple Groups. VIETNAM JOURNAL OF MATHEMATICS [10.1007/s10013-023-00635-1].
A Generalization of Szep’s Conjecture for Almost Simple Groups
Spiga P.
2023
Abstract
We prove a natural generalization of Szep’s conjecture. Given an almost simple group G with socle not isomorphic to an orthogonal group having Witt defect zero, we classify all possible group elements x, y∈ G\ { 1 } with G= NG(⟨ x⟩) NG(⟨ y⟩) , where we are denoting by NG(⟨ x⟩) and by NG(⟨ y⟩) the normalizers of the cyclic subgroups ⟨ x⟩ and ⟨ y⟩ . As a consequence of this result, we classify all possible group elements x, y∈ G\ { 1 } with G= CG(x) CG(y) .
File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
