• April 21, 2017
• Symmetry And Group By Wehrfritz B.A.F.

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Extra info for 2-Generator conditions in linear groups

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The rule is formulated in the following way: x= SVLQ, y = s'v'o', Q(x, y) = svl (s'v'o')i0 When a ULPS is inserted into the truncated pole I „ 1 of another one with v K ) — Qi the suitable rule for this situation is: x = sib^, y = s'v'o', (>(x,y) = sv I (s'v'o')q The result is the one verified in Example 1: Example 1 x = El gat vol # llet y = Joan juga tennis x = The cat wants # some milk y = John plays t e n n i s §{x,y) = El gat vol que Joan jugui a tennis (}(x,y) — The cat wants t h a t John plays t e n n i s 25 But if l(v) ^ q, then thanks to the action of the ghost, the link is also possible.

Cm,d1,d2, • • • ,d m })* —• V*, given by /i(a) = a, a 6 V, /i(cj-) = = Xi, 1 < i < m, fi h(di) = «e(K,) . i < * < m, and g : (V U {ci, c2, • • • ,cm, d1, d2,.. •, dm})* —> V*, given by g(a) — a, a E V, g(ci) = g{di) =e, 1 < i < m. Now we consider the regular language n n R=(\J V{Ci}V+{di}V) »=i U ([J V*{di}V+{Ci}V*). «=i We claim that hpek{L) =g(h-1{L)nR). Indeed, the regular language R assures that the following conditions are satisfied: - The strings in h~l(L) C\R are produced from those strings z in L for which there exists 1 < i < m such that both words x,- and £,(xi)R occur in z, separated by at least one symbol from V, whose inverse morphical images are the symbols c,- and di, respectively, or dj and Cj, respectively, for some j .

Therefore, the generative power of these rules is the following: if n is the number of strata, then the number of sentences is equal to n. 1 Blockade on the right: blockade of object Rules 2 and 4 are not recursive because they insert ULPS without o as an object of X. This absence of object in the resultant string prevents them from being applied again. These rules erase I n I. Therefore, their generative power is minimal, as the number of reaching levels is 2 and the number of forming sentences is also 2.