### Generating Involutions of Infinite Discontinuous Cremona Groups of S_{4} Which Leave a General Cubic Variety Invariant

American Journal of Mathematics, Vol. 53, No. 1 (January 1931), 186-194

Introduction

The present paper derives the equations and obtains the table of characteristics of three types A, B, C of involutorial birational transformations of S_{4}; they are obtained by means of the general cubic variety which remains invariant.

Of these three types the first and second each contain six parameters, and the third more. The product of any two transformations of the set, of the same or of different types, is a non-periodic transformation.

These types and two others discussed previously generate all known transformations which leave the variety V_{3} invariant.

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