منابع مشابه
Sylow Intersections and Fusion
It is common in mathematics for a subject to have its local and global aspects; such is the case in group theory. For example, the structure and embedding of subgroups of a group G may be usefully thought of as part of the local structure of G while the normal subgroups, quotient groups and conjugacy classes are relevant to the global structure of G. Furthermore, the connections between local a...
متن کاملSecondary Sylow Theorems
These theories extend the existent proof of the first sylow theorem (written by Florian Kammueller and L. C. Paulson) by what is often called the second, third and fourth sylow theorem. These theorems state propositions about the number of Sylow p-subgroups of a group and the fact that they are conjugate to each other. The proofs make use of an implementation of group actions and their properties.
متن کاملConsequences of the Sylow Theorems
Proof. Any element of odd order in a symmetric group is an even permutation, so the 3-Sylow and 5-Sylow subgroups of S5 lie in A5. Therefore it suffices to focus on A5. Since |A5| = 60 = 22 · 3 · 5, the 3-Sylow subgroups have size 3 and the 5-Sylows have size 5. Call the numbers n3 and n5. By Sylow III, n3 | 20 and n3 ≡ 1 mod 3, so n3 = 1, 4, or 10. The number of 3-cycles (abc) in A5 is 20, and...
متن کاملSylow Subgroups in Parallel
Sylow subgroups are fundamental in the design of asymptotically efficient group-theoretic algorithms, just as they have been in the study of the structure of Ž . finite groups. We present efficient parallel NC algorithms for finding and conjugating Sylow subgroups of permutation groups, as well as for related problems. Polynomial-time solutions to these problems were obtained more than a dozen ...
متن کاملThe Sylow Theorems
The converse of Lagrange’s theorem is false: if G is a finite group and d|#G, then there may not be a subgroup of G with order d. The simplest example of this is the group A4, of order 12, which has no subgroup of order 6. The Norwegian mathematician Peter Ludwig Sylow [1] discovered that a converse result is true when d is a prime power: if p is a prime number and pk|#G then G must contain a s...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1967
ISSN: 0021-8693
DOI: 10.1016/0021-8693(67)90005-1