The pronorm of a group G is the set P(G) of all elements g ∈ G such that X and Xg are conjugate in 〈X, Xg〉 for every subgroup X of G. In general the pronorm is not a subgroup, but we give evidence of some classes of groups in which this property holds. We also investigate the structure of a generalised soluble group G whose pronorm contains a subgroup of finite index.
ON the PRONORM of A GROUP / Brescia, M.; Russo, A.. - In: BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY. - ISSN 0004-9727. - 104:2(2021), pp. 287-294. [10.1017/S0004972720001549]
ON the PRONORM of A GROUP
Brescia M.;
2021
Abstract
The pronorm of a group G is the set P(G) of all elements g ∈ G such that X and Xg are conjugate in 〈X, Xg〉 for every subgroup X of G. In general the pronorm is not a subgroup, but we give evidence of some classes of groups in which this property holds. We also investigate the structure of a generalised soluble group G whose pronorm contains a subgroup of finite index.File in questo prodotto:
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