Finite Collineation Groups With An Introduction to the Theory of Groups of Oper
Finite Collineation Groups With An Introduction to the Theory of Groups of Oper
Hans Frederik Blichfeldt
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. , a m (m...the first m letters, then Ti~ l would do the reverse. But this has just been proved impossible. Now, a transitive group cannot contain two such sets of letters. Accordingly, G must contain a substitu tion (Vz) which replaces ai by 02, one (F 3 ) which replaces ai by as, etc. , and finally one (V n ) which replaces a\ by a n . (b) Let all those substitutions which leave ai un changed constitute a set H=(Si, 82, . . , Sh), then H is a group. For, the products S a Sb all belong to H. To find the order of H, we arrange the hn substitutions H, HV 2, HV 3, .
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