By Volkodavov V.F., Radionova I.N., Bushkov S.V.

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**Extra info for A 3D analog of problem M for a third-order hyperbolic equation**

**Example text**

Of function v = g(t)/h(t) Then, gives Then 'if' part not finite ~ on u = I/(v-a); k[X0] Every and the kernel (iii) requires field in one v a r i a b l e k(Al), if and If X 0. a proof. v v t ~ >aEk > ~ , set u = v. = k[u]. quotient of of the canonical Ga is k - i s o m o r p h i c homomorphism i__ss 41 given a_~s the zeroes of a p-polynomial Proof. The first assertion over follows the second is verified by the well-known k. 1-(iii), and calculation. ~. 3. Let G As noted in §I, group. 102]) p-polynomials k-group of exponent k-closed (cf.

B = Y(n)AX + FnZ Y, Z e M ~ ( k [ F ] ) the canonical = M(n,B), for some and let generators we can assume of that {x I , M(n,A). n> 0. 5. n e ~ such that (i) M(n,A). M(n,A) if For of pair implies an integer A = A 0 + AIF + ... + Ar Fr ~ ( k [ F ] ) our case. will (ii) be A0 ~ m Let M, we mean (n',A') ~ M(n',A') Hence M the (k) be a smallest = k[F] m. k-form admissible Hence or the M(n,A) = M(n,B). A ~(k[F]) n = 0 of k[F]-module with that in this is an a d m i s s i b l e Conclusion. the X ~(k[F]).

R u s s e ~ type, and let containing K the minimum exists a power of Let G be a k-wound k-group of be a field containing splitting p, d = d(K) field of = pV AUtK_gr(GK) = {x~K EndK_gr(GK) = {yE K : yd = Y }. : x d-I = I} k ~ K1 ~ K2 ing the minimum field of splitting integral power of the last becomes d(Kl) k G. but not Then, there with v ~ I, such that M0reoyer , for any fields over k, -n k(a~ field of G Gk'~(Ga) -n and , none of which contain- G, d(K 2) and a f o r t i o r i an equality whenever is a positve d(K I) ~ d(K2); K2 is separable K1 .

### A 3D analog of problem M for a third-order hyperbolic equation by Volkodavov V.F., Radionova I.N., Bushkov S.V.

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