×

Auflösbare Gruppen mit endlichem Exponenten, deren Untergruppen alle subnormal sind. II. (Soluble groups of finite exponent all subgroups of which are subnormal. II). (German) Zbl 0695.20022

[For part I see the preceding review Zbl 0695.20021.]
The author answers a question of Heineken and Mohamed showing that soluble groups of finite exponent are nilpotent if all their subgroups are subnormal. For the proof it is essential to study carefully certain extensions of elementary abelian p-groups by elementary abelian p-groups.
Reviewer: B.Amberg

MSC:

20F16 Solvable groups, supersolvable groups
20E15 Chains and lattices of subgroups, subnormal subgroups
20F50 Periodic groups; locally finite groups
20F18 Nilpotent groups

Citations:

Zbl 0695.20021
PDFBibTeX XMLCite
Full Text: Numdam EuDML

References:

[1] H. Heineken - I.J. Mohamed , Non-nilpotent groups with normalizer condition , Proc. Sec. Internat. Conf. Theory of Groups 1973 , Lecture Notes in Mathematics , 372 , pp. 357 - 360 , Springer-Verlag , Berlin , 1974 . MR 357611 | Zbl 0286.20033 · Zbl 0286.20033
[2] W. Möhres , Auflösbare Gruppen mit endlichem Exponenten, deren Untergruppen alle subnormat sind - I , Rend. Sem. Mat. Univ. Padova , 81 ( 1989 ), pp. 255 - 268 . Numdam | MR 1020199 | Zbl 0695.20021 · Zbl 0695.20021
[3] B.H. Neumann , Groups covered by permutable subsets , J. London Math. Soc. , 29 ( 1954 ), pp. 236 - 248 . MR 62122 | Zbl 0055.01604 · Zbl 0055.01604 · doi:10.1112/jlms/s1-29.2.236
[4] D.J.S. Robinson , A Course in the Theory of Groups , Springer-Verlag , New York - Heidelberg - Berlin ( 1982 ). MR 648604 | Zbl 0483.20001 · Zbl 0483.20001
[5] J.E. Roseblade , On groups in which every subgroup is subnormal , J. Algebra , 2 ( 1965 ), pp. 402 - 412 . MR 193147 | Zbl 0135.04901 · Zbl 0135.04901 · doi:10.1016/0021-8693(65)90002-5
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.