Second cohomology group

Dear Forum,

Let A be an associative division algebra (i.e. a skew field), G a subgroup of the multiplicative group of A and E an extension of the additive group A+ of A by G such that G acts on A+ by multiplication in A. Is it true that E always splits? In other words is H^(G,A)=0? Best wishes, V.D. Mazurov

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Could you please use the LaTeX environment when writing math formulae? –  Michele Triestino Sep 17 '10 at 6:56
If $A$ is a finite field, the answer is yes (see Serre's Local Fields, Prop. 8). But you probably know this already. –  Amritanshu Prasad Nov 23 '10 at 6:27