A subgroup X of a group G is said to be pronormal if for each element g of G the subgroups X and Xg are conjugate in (X, Xg). The aim of this paper is to study pronormality and some close embedding properties, like weak normality and weak pronormality. In particular, it is proved that these properties can be countably detected, and the behaviour of groups which are rich in (generalized) pronormal subgroups is investigated.
Pronormality in group theory / de Giovanni, F.; Trombetti, M.. - In: ADVANCES IN GROUP THEORY AND APPLICATIONS. - ISSN 2499-1287. - 9:(2020), pp. 123-149. [10.32037/agta-2020-005]
Pronormality in group theory
de Giovanni F.
;Trombetti M.
2020
Abstract
A subgroup X of a group G is said to be pronormal if for each element g of G the subgroups X and Xg are conjugate in (X, Xg). The aim of this paper is to study pronormality and some close embedding properties, like weak normality and weak pronormality. In particular, it is proved that these properties can be countably detected, and the behaviour of groups which are rich in (generalized) pronormal subgroups is investigated.File in questo prodotto:
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