Crossed Extensions
Copyright policy )Crossed Extensions
We develop a natural five term exact sequence relating the second and third cohomology of groups. We show that this sequence is the proper framework for the problem of realizing an abstract kernel. As an application, we give an interpretation of the third cohomology of a group in terms of crossed sequences.
Homological methods in group theory, Obstruction theory in algebraic topology, Extensions, wreath products, and other compositions of groups, Ext and Tor, generalizations, Künneth formula (category-theoretic aspects), MacLane-Whitehead obstruction, crossed sequences, G-crossed extension, crossed module, congruence classes of extensions, abstract kernels, inflation maps
Homological methods in group theory, Obstruction theory in algebraic topology, Extensions, wreath products, and other compositions of groups, Ext and Tor, generalizations, Künneth formula (category-theoretic aspects), MacLane-Whitehead obstruction, crossed sequences, G-crossed extension, crossed module, congruence classes of extensions, abstract kernels, inflation maps
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