A group G is said to be ambivalent if every element of G is conjugate to its inverse. In the present paper, we investigate several properties of ambivalent groups, establishing structural restrictions when the group is either nilpotent or periodic. Additionally, we examine the fixed-point-free case and provide a presentation of the group when it is not 2-nilpotent. This investigation sheds light on the structure of ambivalent groups that possess a strongly embedded subgroup.
On ambivalent groups
Delizia, Costantino;Monetta, Carmine
;Nicotera, Chiara
2025
Abstract
A group G is said to be ambivalent if every element of G is conjugate to its inverse. In the present paper, we investigate several properties of ambivalent groups, establishing structural restrictions when the group is either nilpotent or periodic. Additionally, we examine the fixed-point-free case and provide a presentation of the group when it is not 2-nilpotent. This investigation sheds light on the structure of ambivalent groups that possess a strongly embedded subgroup.File in questo prodotto:
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