The rank of the factor-group modulo the hypercenter and the rank of the some hypocenter of a group

Leonid Kurdachenko; Javier Otal

Open Mathematics (2013)

  • Volume: 11, Issue: 10, page 1732-1741
  • ISSN: 2391-5455

Abstract

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We compare the special rank of the factors of the upper central series and terms of the lower central series of a group. As a consequence we are able to show some generalizations of a theorem of Reinhold Baer.

How to cite

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Leonid Kurdachenko, and Javier Otal. "The rank of the factor-group modulo the hypercenter and the rank of the some hypocenter of a group." Open Mathematics 11.10 (2013): 1732-1741. <http://eudml.org/doc/269301>.

@article{LeonidKurdachenko2013,
abstract = {We compare the special rank of the factors of the upper central series and terms of the lower central series of a group. As a consequence we are able to show some generalizations of a theorem of Reinhold Baer.},
author = {Leonid Kurdachenko, Javier Otal},
journal = {Open Mathematics},
keywords = {Upper central series; Lower central series; Schur theorem; Baer theorem; Finite special rank; Generalized radical group; Hypercentral group; upper central series; lower central series; groups of finite special rank; generalized radical groups; hypercentral groups; locally finite groups},
language = {eng},
number = {10},
pages = {1732-1741},
title = {The rank of the factor-group modulo the hypercenter and the rank of the some hypocenter of a group},
url = {http://eudml.org/doc/269301},
volume = {11},
year = {2013},
}

TY - JOUR
AU - Leonid Kurdachenko
AU - Javier Otal
TI - The rank of the factor-group modulo the hypercenter and the rank of the some hypocenter of a group
JO - Open Mathematics
PY - 2013
VL - 11
IS - 10
SP - 1732
EP - 1741
AB - We compare the special rank of the factors of the upper central series and terms of the lower central series of a group. As a consequence we are able to show some generalizations of a theorem of Reinhold Baer.
LA - eng
KW - Upper central series; Lower central series; Schur theorem; Baer theorem; Finite special rank; Generalized radical group; Hypercentral group; upper central series; lower central series; groups of finite special rank; generalized radical groups; hypercentral groups; locally finite groups
UR - http://eudml.org/doc/269301
ER -

References

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  8. [8] Lubotzky A., Mann A., Powerful p-groups. I. Finite groups, J. Algebra, 1987, 105(2), 484–505 http://dx.doi.org/10.1016/0021-8693(87)90211-0[Crossref] Zbl0626.20010
  9. [9] Makarenko N.Yu., Rank analogues of Hall’s and Baer’s theorems, Siberian Math. J., 2000, 41(6), 1137–1140 http://dx.doi.org/10.1023/A:1004828422007[Crossref] 
  10. [10] Schur J., Über die Darstellungen der endlichen Gruppen durch gebrochene lineare substitutionen, J. Reine Angew. Math., 1904, 127, 20–50 Zbl35.0155.01
  11. [11] Wiegold J., Groups with boundedly finite classes of conjugate elements, Proc. Roy. Soc. London Ser. A, 1956, 238(1214), 389–401 Zbl0077.03002
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