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. In a previous paper [8], we have defined a sequence of cohomology groups Hr(G, A) defined when G is a locally compact group and A is an abelian locally compact group on which G acts continuously as a group of automorphisms. The structure of these cohomology groups, particularly the two dimensional groups, was discussed in this paper; here we shall discuss the structure of these cohomology low dimensional groups under more general assumptions on G. Explicitly we shall be concerned with the class of locally compact groups G which have the property that GjG0 is compact (where G0 is the connected component of the identity in G). For simplicity we shall call such groups almost connected. When G is in fact connected, then we can obtain more explicit information by use of a principal series of normal subgroups in G discussed by Iwasawa [3], in conjunction with a spectral sequence. Also we shall introduce the notion of splitting groups and use them to discuss the problem of topologizing the two dimensional group H2(G,A) of extensions of G by A. The notation and terminology used will be that of [8].

Extensions and low dimensional cohomology theory of locally compact groups. I, II