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

flag	asked Sep 17 2010 at 2:46 Victor Mazurov 41●1

	Could you please use the LaTeX environment when writing math formulae? – Michele Triestino Sep 17 2010 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 2010 at 6:27