Geodesic
1-Cohomology and Splitting of Group Extensions
Canadian mathematical bulletin, Tome 19 (1976) no. 3, pp. 369-371

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The object of this note is to give simpler proofs of a splitting theorem of Gaschütz [1] and a related theorem for groups with operators by using cross-homomorphisms (1-cocycles) instead of 2-cohomology.We recall that a cross-homomorphism or 1-cocycle from a group E to an abelian normal subgroup N of E is a map f from E to N such that f(ab)=(f(a))b f(b) for all a, b ∈ E where superscript denotes conjugation. Cocycles f and h are equivalent if for some n ∈ N have h(e)=n e f(e)n -1 for all e ∈ E. 
Pandya, G. N.; Bercov, R. D. 1-Cohomology and Splitting of Group Extensions. Canadian mathematical bulletin, Tome 19 (1976) no. 3, pp. 369-371. doi: 10.4153/CMB-1976-057-7
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     title = {1-Cohomology and {Splitting} of {Group} {Extensions}},
     journal = {Canadian mathematical bulletin},
     pages = {369--371},
     year = {1976},
     volume = {19},
     number = {3},
     doi = {10.4153/CMB-1976-057-7},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1976-057-7/}
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