GROUPS IN WHICH ALL SUBGROUPS OF INFINITE RANK ARE SUBNORMAL
Glasgow mathematical journal, Tome 46 (2004) no. 1, pp. 83-89
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Let $G$ be a locally soluble-by-finite group in which every non-subnormal subgroup has finite rank. It is proved that either $G$ has finite rank or $G$ is soluble and locally nilpotent (and even a Baer group). On the other hand, a group $G$ is constructed that has infinite rank and satisfies the given hypothesis, but does not have every subgroup subnormal.
KURDACHENKO, LEONID A.; SMITH, HOWARD. GROUPS IN WHICH ALL SUBGROUPS OF INFINITE RANK ARE SUBNORMAL. Glasgow mathematical journal, Tome 46 (2004) no. 1, pp. 83-89. doi: 10.1017/S0017089503001551
@article{10_1017_S0017089503001551,
author = {KURDACHENKO, LEONID A. and SMITH, HOWARD},
title = {GROUPS {IN} {WHICH} {ALL} {SUBGROUPS} {OF} {INFINITE} {RANK} {ARE} {SUBNORMAL}},
journal = {Glasgow mathematical journal},
pages = {83--89},
year = {2004},
volume = {46},
number = {1},
doi = {10.1017/S0017089503001551},
url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089503001551/}
}
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%0 Journal Article %A KURDACHENKO, LEONID A. %A SMITH, HOWARD %T GROUPS IN WHICH ALL SUBGROUPS OF INFINITE RANK ARE SUBNORMAL %J Glasgow mathematical journal %D 2004 %P 83-89 %V 46 %N 1 %U http://geodesic.mathdoc.fr/articles/10.1017/S0017089503001551/ %R 10.1017/S0017089503001551 %F 10_1017_S0017089503001551
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