Theory and Applications of Finite Groups

Abstract

THE English student is fortunate in having, in his own language, a series of excellent treatises on the difficult theory of groups. The present one is welcome as a record of progress, even in what may be ealled the elements of the sublect, and as an originai work by three distinguished experts. It is divided into three parts, for each of whieh one author is mainly responsible. Part i., by Prof. G. A. Miller, deals with the generai properties of groups, beginning with substitution-groups, and going on to the abstract definition by generators; there are speciai chapters on Abelian groups, on groups of order p^m with p prime, on the poiyhedrai groups, on isomorphisms, and on solvable groups. Part ii., by Prof. H. E. Bhichfeldt, is on linear groups, and a valuable summary of the present stage of that theory; in particular, there is a chapter on characteristics. Part iii., by Prof. L. E. Dickson, is on applications, and is naturally of a more eiementary charaeter; there are three. chapters on the Galoisian theory of equations, one on rule and compass constructions, one on the inflexions of a piane cubie, one on the 27 iines of a cubie surface, and one which is a scrap on solutions of equations by a standard form F(z, k) = o, invoiving one parameter.

Theory and Applications of Finite Groups.

By Profs. G. A. Miller H. F. Blichfeldt L. E. Dickson. Pp. xvii + 390. (New York: John Wiley and Sons, Inc.; London: Chapman and Hall, Ltd., 1916.) Price 17s. net.