Groups with normal subgroups possessing subnormal complements
HTML articles powered by AMS MathViewer
- by K. H. Toh
- Proc. Amer. Math. Soc. 41 (1973), 378-380
- DOI: https://doi.org/10.1090/S0002-9939-1973-0325787-1
- PDF | Request permission
Abstract:
J. Wiegold has characterized groups in which every normal subgroup is a direct factor as the restricted direct products of simple groups. In this paper, it is proved that for a group $G$ to have the structure above, it is sufficient that every normal subgroup of $G$ has a subnormal complement in $G$.References
- S. N. Černikov, Groups with systems of complemented subgroups, Amer. Math. Soc. Transl. (2) 17 (1961), 117–152. MR 0124402, DOI 10.1090/trans2/017/04
- Carlton Christensen, Complementation in groups, Math. Z. 84 (1964), 52–69. MR 163964, DOI 10.1007/BF01112209
- C. Christensen, Groups with complemented normal subgroups, J. London Math. Soc. 42 (1967), 208–216. MR 207834, DOI 10.1112/jlms/s1-42.1.208
- Nelson Terry Dinerstein, Finiteness conditions in groups with systems of complemented subgroups, Math. Z. 106 (1968), 321–326. MR 235028, DOI 10.1007/BF01110279
- James Wiegold, On direct factors in groups, J. London Math. Soc. 35 (1960), 310–320. MR 130299, DOI 10.1112/jlms/s1-35.3.310
- D. Ī. Zaĭcev, Normally factorizable groups, Dokl. Akad. Nauk SSSR 197 (1971), 1007–1009 (Russian). MR 0285602
Bibliographic Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 41 (1973), 378-380
- MSC: Primary 20F30
- DOI: https://doi.org/10.1090/S0002-9939-1973-0325787-1
- MathSciNet review: 0325787