Finite Collineation Groups With An Introduction to the Theory of Groups of Oper

Cover 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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