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Abbreviations
- G′ :
-
commutator subgroup of the groupG=subgroup ofG, generated by allx −1y−1xy wherex andy are elements ofG
- \(X \subseteq Y\) :
-
X is a subgroup of the groupY
- X⊂Y :
-
X is a proper subgroup ofY
- G×H :
-
direct product of the groupsG andH
- 〈...〉:
-
subgroup generated by...,
- AB :
-
set of all elementsab wherea is an element of the subgroupA andb is an element of the subgroupB (AB is a group if and only ifAB=BA)
- X G :
-
largest normal subgroup ofG contained in the subgroupX
- cX :
-
centralizer ofX
- nX :
-
normalizer ofX
- ζG :
-
center ofG
- factor:
-
epimorphic image of a subgroup
- chief factor:
-
minimal normal subgroup of an epimorphic image
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The author gratefully acknowledges the hospitality of the University of Frankfurt am Main, Germany, during the summer of 1970 when most of this research was done.
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Amberg, B. Abelian factorizations of infinite groups. Math Z 123, 201–214 (1971). https://doi.org/10.1007/BF01114789
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DOI: https://doi.org/10.1007/BF01114789