Conjugate group elements

LetAandAbetwoelementsinagroup.ThenZ AZ = B will be equal to some element in the group. The element B is called the similarity transform of A by X and A and B may be said to be conjugate. Conjugate group elements have the following properties ... 

Prove that if P and R are group elements each conjugate to the element Q, then P and R are conjugate to each other. 

The organometallic chemistry of alkynylcyclopropanes involves primarily the formation and reactions of carbon-metal er-bonds. Metals come essentially from the main group elements, with lithium playing a major role. The two metallation sites are the cyclopropyl and the acetylenic positions, which are expected to differ considerably in their acidity values (t-butylacetylene, pKa = 25230, cyclopropane, pKa = 46183) but less in the reactivity of their metal conjugated bases towards electrophiles. 

Cyano compounds (nitriles) R-C N 2260-2240 (w) (aliphatic) 2240-2220 (m) (aromatic, conjugated) Electronegative elements a-to the CsN group reduce the intensity of the absorption... 

A class is a complete set of elements, in our case symmetry operations, of the group that are conjugate to one another (in mathematics they are usually called conjugacy class). Elements A and B of a group are conjugates, if there is some group element, Z, for which... 

Every element is conjugate with itself Thus for any particular group element A there must be at least one element X such that A = X AX. 

The synthesis and experimental study of metastable compounds bearing conjugated Si=E bonds (E = main group element) is still very limited. In fact, compounds having conjugated Si=Si bonds are hitherto unknown. The first metastable compounds, 35a and 35b, containing conjugated Si=E bonds (E = P, N), were synthesized by Niecke et al. [7, 8] and West et al. [34]. 

In compounds of main group elements, the band ranges from 870 to 1285 cm [6,102]. In transition metal compounds, it is observed from 810-1385 cm [50,53]. If the C=S double-bond character is low, as seen for a free dithiocarboxylate anion, the stretching shifts to lower wavenumbers [38,124]. This is also true for complexes where the dithiocarboxylate hgand is conjugated with an a,p-unsaturated double-bond, and/or complexes with a C=S - H hydrogen bond [50]. If the C=S double-bond character is high in the dithiocar-boxyUc acid salt, the vCS vibrations appear at 1100-1200 cm [82,95]. 

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