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- W4251027316 abstract "The extension problem for abelian groups [as a special case of the general group theoretical problem formulated by O. Schreier] consists in determining the group from a subgroup and the corresponding quotient group. The classical way of discussing extensions is via factor sets. It was a profound discovery of R. Baer's, that the extensions—under a suitable equivalence relation—themselves formed a group Ext, the group of extensions. It is the study of this group which is our main topic in this chapter.An intimate relationship between groups of extensions and groups of homomorphisms has been pointed out by Eilenberg and Mac Lane [1]; this led to the interpretation of Ext as the socalled derived functor of Horn, and has been exploited extensively by Cartan and Eilenberg [1]. Ext can be discussed in various ways; we shall rely upon the elegant method of Mac Lane [3].Our main objective is to discover the group theoretical properties of Ext (C, A), its dependence upon the groups A and C, and its relation with known constructions. Some of our goals are beyond the limits of our methods, but a good deal of information can be obtained about the general case which settles the problem in a number of special cases. The exact sequences connecting Horn and Ext, their generalizations, and the theory of cotorsion groups are the most relevant results in this chapter." @default.
- W4251027316 created "2022-05-12" @default.
- W4251027316 date "1970-01-01" @default.
- W4251027316 modified "2023-09-25" @default.
- W4251027316 title "IX Groups of Extensions" @default.
- W4251027316 doi "https://doi.org/10.1016/s0079-8169(08)62808-1" @default.
- W4251027316 hasPublicationYear "1970" @default.
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