<abstract xmlns="http://www.w3.org/1999/xhtml">Y. Li gave a characterization of the class of finite soluble groups in which every subnormal subgroup is normal by means of <italic>NE</italic>-subgroups: a subgroup <italic>H</italic> of a group <italic>G</italic> is called an <italic>NE</italic>-subgroup of <italic>G</italic> if <italic>NG</italic>(<italic>H</italic>) ∩ <italic>HG</italic> = <italic>H</italic>. We obtain a new characterization of these groups related to the local Wielandt subgroup. We also give characterizations of the classes of finite soluble groups in which every subnormal subgroup is permutable or Sylow permutable in terms of <italic>NE</italic>-subgroups.</abstract>

Y. Li gave a characterization of the class of finite soluble groups in which every subnormal subgroup is normal by means of NE-subgroups: a subgroup H of a group G is called an NE-subgroup of G if NG(H) ∩ HG = H. We obtain a new characterization of these groups related to the local Wielandt subgroup. We also give characterizations of the classes of finite soluble groups in which every subnormal subgroup is permutable or Sylow permutable in terms of NE-subgroups.

Finite groups in which normality, permutability or Sylow permutability is transitive

Institute of Mathematics, University of Białystok, 15-267 Białystok, Akademicka 2, Poland.

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Y. Li gave a characterization of the class of finite soluble groups in which every subnormal subgroup is normal by means of NE-subgroups: a subgroup H of a...

Finite groups in which normality, permutability or Sylow permutability is transitive

Published Online: Dec 22, 2015

Page range: 137 - 146

Received: Apr 10, 2013

Accepted: Oct 14, 2013

DOI: https://doi.org/10.2478/auom-2014-0055

Keywords
-subgroup, -group, -group, -group, local Wielandt subgroup

© 2014 Izabela Agata Malinowska, published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Finite groups in which normality, permutability or Sylow permutability is transitive

Published Online: Dec 22, 2015

Page range: 137 - 146

Received: Apr 10, 2013

Accepted: Oct 14, 2013

DOI: https://doi.org/10.2478/auom-2014-0055

Keywords-subgroup, -group, -group, -group, local Wielandt subgroup

© 2014 Izabela Agata Malinowska, published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
-subgroup, -group, -group, -group, local Wielandt subgroup