Diagonal subgroup

Using both pX and pX we obtain, according to Equation (3.5), an action of the diagonal subgroup... 

Remark (The case of an achiral skeleton) Now we assume R P, i.e. an achiral skeleton. We indicate the set of substitutable positions with X mid the set of substituents with Y = Y f,iiY. The corresponding actions of the point group are pX and pT. They define induced actions of the diagonal subgroups A(P x P) and A(R x R) on the set Y of distributions, with their sets of orbits... 

Theorem. Let M be a subgroup of GL fc). The elements of M can be simuhan-eously diagonalized iff the group scheme G corresponding to M is diagonalizable. 

As for magnesium oxide, it should be mentioned that this drops out of the dependence for alkaline-earth oxides, because the chemical properties of magnesium are closer to those of aluminium than to the properties of other members of alkali-metal subgroup (it is the so-called diagonal periodicity). The dependence of oxide solubilities against their melting points exists for the... 

Inspection of Table 13-2 reveals that it is not symmetric across its principal diagonal. For example, CF = B, and EC = A, this is not an abelian group. One might inquire whether this group is the smallest that we can set up for the ammonia model. Inspection of the multiplication table should convince the reader that the following subsets meet the requirements for a group E, D, F E, A E, B E, C. These subgroups can be... 

On confining attention to permutations of the subgroup S2 (i.e. considering only (12) and the identity), the basis functions p l and behave exactly like the basis functions < pl and respectively that carry standard irreps of S2 and the corresponding matrices appear in block form, the diagonal blocks being the (1-element) matrices already known for S2. 

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