Bireflectionality in Classical Groups

Canadian Journal of Mathematics - Tập 29 Số 6 - Trang 1157-1162 - 1977
Erich W. Ellers1
1University of Toronto, Toronto, Ontario

Tóm tắt

The motion groups of the real Euclidean plane and of the elliptic plane, the group of projectivities of a line, the projective general linear group PGL2(K), some orthogonal groups O3(K, Q) with char K = 2 (see [8]), are all bireflectional (zweispiegelig). There can be no doubt that bireflectional groups are of prime importance in any theory of groups that are generated by involutions. A brief look into F. Bachmann's book [1] gives convincing evidence.

Từ khóa


Tài liệu tham khảo

Lingenberg, 1960, Die orthogonalen Gruppen Oz(K, Q) ùber Kôrpern von Charakteristik, 21, 371

Coxeter, 1974, Regular complex polytopes

O'Meara, 1969, Math. Z, Group-theoretic characterization of transvections using CDC,, 110, 385

Coxeter, 1973, Regular polytopes,

Ellers E. W. , Decomposition of orthogonal, symplectic, and unitary isometries into simple isometries, Abh. Math. Sem. Univ. Hamburg Jfi

Wiener, 1893, Ber. Verh. kgl. Sachs. Ges. Wiss. Leipzig, math.-nat. Kl, Ùber Gruppen vertauschbarer zweispiegeliger Verwandtschaften,, 45, 555

Dieudonné, 1955, La géométrie des groupes classiques

Ellers E. W. Decomposition of equiaffinities into reflections, to appear, Geometriae Dedicata.

Dienst, 1972, Bewegungsgruppen projektiv-metrischer Ebenen von Char., 050, 135

Veblen, 1946, Projective geometry, Vol. II

10.1007/978-3-642-65537-1