## Primitive Groups which Contain Substitutions of Prime Order P and of Degree 6p Or 7p |

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2pfl 3p letters 3p+l 3pfl alternating constituent alternating group belongs constituent groups constituent of degree contains a substitution contradict Theorems cycles on letters cyclic group decree degree 2pf4 degree 6p degree 7p+8 degree and order degree l4 degree of F degree p+2 doubly transitive group F of degree F show fix the 2p fixes one letter fixes the letter gree group of class group of degree group of order groups of F impossible by Theorem imprimitive constituent integer invariant subgroup ion of order itive constituent Mathieu group metacyclic group negative substitution order f order l6 p-tl permute positive groups possible partitions prime order proup Ptl Ptl q cycles quotient group representation simply Isomorphic simply transitive primitive stituent of degree subgroup of order subgroup that fixes substitution of order substitution of prime symmetric group systems of imprimitivity transitive of degree transitive primitive group uent of degree