By Tripathi M. M., Kim J., Kim S.

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Restriction to V defines a functor from the category of G-sets to the category of V -sets, which maps sums into sums and products into products, more generally: direct and inverse limits into direct resp. inverse limits. Thus it defines ring homomorphism Q(G) ~ Q(V), especially a multiplicative map f(G) ~ f(V) which is easily seen to be an Q(G)-module-homomorphism, if f(V) is considered as an Q(G)-module via Q(G) ~ Q(V). The restriction functor has a left and a right adjoint. The left adjoint maps a V-set S onto the G-set G x uS, the set of V-orbits in G x S for the V-action: u E V, g E G, SE S = u(g,s) = (gu- 1, us) with the well-defined G-action g' (g,s)- = (g'g,s)-((g,s)- the V-orbit of(g,s)EG x S).

The group GB is N H(D)",KI K. The inclusion isomorphism of N H(D)/N K(D)", onto GB together wirh the above isomorphism of C H(D)w

Math. Soc. 22 (1969). 460-465. MR 39 #4213. UNIVERSITY OF SYDNEY. AUSTRALIA A Clifford Theory for Blocks E. C. Dade Everybody knows about the theory of Clifford [2J relating the characters of a finite group H to those of a normal subgroup K of H and to projective characters of certain subgroups of G = H/ K. The factor group G acts by conjugation on the family of all irreducible \j-characters of K, where \j is an algebraically closed field. Let Gq> be the subgroup of G fixing such a character cp.

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A basic inequality for submanifolds in locally conformal almost cosymplectic manifolds by Tripathi M. M., Kim J., Kim S.


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