Geodesic
GROUPS OF INFINITE RANK IN WHICH NORMALITY IS A TRANSITIVE RELATION
Glasgow mathematical journal, Tome 56 (2014) no. 2, pp. 387-393

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DOI

A group is called a T-group if all its subnormal subgroups are normal. It is proved here that if G is a periodic (generalized) soluble group in which all subnormal subgroups of infinite rank are normal, then either G is a T-group or it has finite rank. It follows that if G is an arbitrary group whose Fitting subgroup has infinite rank, then G has the property T if and only if all its subnormal subgroups of infinite rank are normal.
DOI : 10.1017/S0017089513000323
Mots-clés : 20E15 
FALCO, M. DE; GIOVANNI, F. DE; MUSELLA, C.; SYSAK, Y. P. GROUPS OF INFINITE RANK IN WHICH NORMALITY IS A TRANSITIVE RELATION. Glasgow mathematical journal, Tome 56 (2014) no. 2, pp. 387-393. doi: 10.1017/S0017089513000323
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     title = {GROUPS {OF} {INFINITE} {RANK} {IN} {WHICH} {NORMALITY} {IS} {A} {TRANSITIVE} {RELATION}},
     journal = {Glasgow mathematical journal},
     pages = {387--393},
     year = {2014},
     volume = {56},
     number = {2},
     doi = {10.1017/S0017089513000323},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089513000323/}
}
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