Geometry And Collineation Groups of the Finite Projective Plane Pg 22
Geometry And Collineation Groups of the Finite Projective Plane Pg 22
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Suppose n to be less than N/3 . G must then contain m> N/3 collineations of determinant d where d is either i or r. If T be any collineation in G of determinant d 2 the products of the m collineations of determinant d by T are m>N/3 distinct collineations of determi riant unity in G, contrary to supposition. Since n is neither less nor greater than N/3 it follows that n= N/3 The Group of Determinant Unity. By Theorem 5 the group G 60480 has a self-con- jugate subgroup of determinant unity of or...der 60480/3=20160. In §4 it was shown that all collineations of types I a, III, V and those of type I of period 7 and type I of period 5 were of determinant unity. Hence the Group 20160 of determinant unity contains the following collineations: The identical collineation 1 All collineations of type I 3 2240 Those collineations of type Ii which are of period 5, (1-3 of the total number) 8064 Those collineations of type I which are of period 7, (3-10 of the total number) 5760 All collineations of type III 3780 All collineations of type V 315 20160 The group will be designated as above by G 20180 .
What to read after Geometry And Collineation Groups of the Finite Projective Plane Pg 22?
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To quickly assess the difficulty of the text, read a short excerpt:
Suppose n to be less than N/3 . G must then contain m> N/3 collineations of determinant d where d is either i or r. If T be any collineation in G of determinant d 2 the products of the m collineations of determinant d by T are m>N/3 distinct collineations of determi riant unity in G, contrary to supposition. Since n is neither less nor greater than N/3 it follows that n= N/3 The Group of Determinant Unity. By Theorem 5 the group G 60480 has a self-con- jugate subgroup of determinant unity of or...der 60480/3=20160. In §4 it was shown that all collineations of types I a, III, V and those of type I of period 7 and type I of period 5 were of determinant unity. Hence the Group 20160 of determinant unity contains the following collineations: The identical collineation 1 All collineations of type I 3 2240 Those collineations of type Ii which are of period 5, (1-3 of the total number) 8064 Those collineations of type I which are of period 7, (3-10 of the total number) 5760 All collineations of type III 3780 All collineations of type V 315 20160 The group will be designated as above by G 20180 .
What to read after Geometry And Collineation Groups of the Finite Projective Plane Pg 22?
You can find similar books in the "Read Also" column, or choose other free books by Ulysses Grant Mitchell to read onlineMoreLess
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