Bulletin of the American Mathematical Society Volume 12 - Brossura

Society, American Mathematical

Brossura

ISBN 10: 1130515702 ISBN 13: 9781130515701

Casa editrice: RareBooksClub.com, 2012

Riassunto

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1906 Excerpt: ...considered above. If G contained three invariant operators of order 2, while the remaining 10 formed a single set of conjugates, the three invariant operators would generate the four group. As any one of the remaining operators of order 2 and this four group would generate the group of order 8 which has 7 operators of order 2, the remaining operators could be arranged in distinct sets of four operators, which is evidently impossible. If G contained two invariant operators, their product would also be invariant and hence there could not be a complete set of eleven conjugates. It only remains therefore to consider the case where 6r contains a single invariant operator of order 2 while the remaining 12 constitute a complete set of conjugates. It will be found that there are groups which come under this ease. Hence there are groups containing exactly 13 operators of order 2 in which these operators form sets of conjugates containing any of the following numbers of operators: 13; 1, 2, 10; 1, 6, 6; 1, 12. § 5. Groups in which there is a Complete Set of Twelve Conjugates of Order 2. Since such a G contains an invariant operator of order 2, it contains six conjugate four groups and transforms them according to a transitive substitution group T of degree 6. If the operators H of G which correspond to the identity of T included more than one operator of order 2, these six subgroups of order 4 would generate a group of order 2"' involving thirteen operators of order 2. As this is impossible, T contains a complete set of either three or six conjugate substitutions of order 2 and of degree 6, corresponding to the operators of order 2 in G. In the former case these three conjugate substitutions of T cannot be commutative, since all the operators of order 2 in ...

Su questa edizione

• Editore: RareBooksClub.com
• Data di pubblicazione: 2012
• ISBN 10: 1130515702
• ISBN 13: 9781130515701
• Rilegatura: Copertina flessibile
• Numero di pagine: 206