On non-periodic groups whose finitely generated subgroups are either permutable or pronormal

L. A. Kurdachenko; I. Ya. Subbotin; T. I. Ermolkevich

Mathematica Bohemica (2013)

  • Volume: 138, Issue: 1, page 61-74
  • ISSN: 0862-7959

Abstract

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The current article considers some infinite groups whose finitely generated subgroups are either permutable or pronormal. A group G is called a generalized radical, if G has an ascending series whose factors are locally nilpotent or locally finite. The class of locally generalized radical groups is quite wide. For instance, it includes all locally finite, locally soluble, and almost locally soluble groups. The main result of this paper is the followingTheorem. Let G be a locally generalized radical group whose finitely generated subgroups are either pronormal or permutable. If G is non-periodic then every subgroup of G is permutable.

How to cite

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Kurdachenko, L. A., Subbotin, I. Ya., and Ermolkevich, T. I.. "On non-periodic groups whose finitely generated subgroups are either permutable or pronormal." Mathematica Bohemica 138.1 (2013): 61-74. <http://eudml.org/doc/252497>.

@article{Kurdachenko2013,
abstract = {The current article considers some infinite groups whose finitely generated subgroups are either permutable or pronormal. A group $G$ is called a generalized radical, if $G$ has an ascending series whose factors are locally nilpotent or locally finite. The class of locally generalized radical groups is quite wide. For instance, it includes all locally finite, locally soluble, and almost locally soluble groups. The main result of this paper is the followingTheorem. Let $G$ be a locally generalized radical group whose finitely generated subgroups are either pronormal or permutable. If $G$ is non-periodic then every subgroup of $G$ is permutable.},
author = {Kurdachenko, L. A., Subbotin, I. Ya., Ermolkevich, T. I.},
journal = {Mathematica Bohemica},
keywords = {pronormal subgroup; permutable subgroup; finitely generated subgroup; abnormal subgroup; generalized radical groups; pronormal subgroups; permutable subgroups; finitely generated subgroups; abnormal subgroups},
language = {eng},
number = {1},
pages = {61-74},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On non-periodic groups whose finitely generated subgroups are either permutable or pronormal},
url = {http://eudml.org/doc/252497},
volume = {138},
year = {2013},
}

TY - JOUR
AU - Kurdachenko, L. A.
AU - Subbotin, I. Ya.
AU - Ermolkevich, T. I.
TI - On non-periodic groups whose finitely generated subgroups are either permutable or pronormal
JO - Mathematica Bohemica
PY - 2013
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 138
IS - 1
SP - 61
EP - 74
AB - The current article considers some infinite groups whose finitely generated subgroups are either permutable or pronormal. A group $G$ is called a generalized radical, if $G$ has an ascending series whose factors are locally nilpotent or locally finite. The class of locally generalized radical groups is quite wide. For instance, it includes all locally finite, locally soluble, and almost locally soluble groups. The main result of this paper is the followingTheorem. Let $G$ be a locally generalized radical group whose finitely generated subgroups are either pronormal or permutable. If $G$ is non-periodic then every subgroup of $G$ is permutable.
LA - eng
KW - pronormal subgroup; permutable subgroup; finitely generated subgroup; abnormal subgroup; generalized radical groups; pronormal subgroups; permutable subgroups; finitely generated subgroups; abnormal subgroups
UR - http://eudml.org/doc/252497
ER -

References

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