Loading...
Please wait, while we are loading the content...
Similar Documents
Sylow Theory: The Theorems
| Content Provider | Scilit |
|---|---|
| Author | Anderson, Marlow Feil, Todd |
| Copyright Year | 2014 |
| Description | We will now apply the theory from the last chapter to obtain the Sylow theorems. These theorems will enable us to understand the p-subgroups of any finite group, taken one prime p at a time. Throughout this chapter we will assume that G is a finite group, and that it has pnm elements, where p is a prime, and m is relatively prime to p. We will be able to show that G has subgroups of order pn (called Sylow p-subgroups), that all such subgroups are isomorphic, and we will often be able to count how many of these subgroups there are. Given our finite group G with pnm elements, suppose that H is a subgroup of G and a p-group. We then say that H is a p-subgroup of G. We call H a Sylow p-subgroup of G if it is a maximal p-subgroup of G. That is, if H is a Sylow p-subgroup of G and K is a p-subgroup of G that contains H, then K = H. Because G is a finite group, it is then obvious that every p-subgroup is contained in a Sylow p-subgroup. What is not yet obvious is how many elements a Sylow p-subgroup has. Book Name: A First Graduate Course in Abstract Algebra |
| Related Links | https://content.taylorfrancis.com/books/download?dac=C2013-0-28248-0&isbn=9780429156281&doi=10.1201/b17673-42&format=pdf |
| Ending Page | 341 |
| Page Count | 10 |
| Starting Page | 332 |
| DOI | 10.1201/b17673-42 |
| Language | English |
| Publisher | Informa UK Limited |
| Publisher Date | 2014-11-07 |
| Access Restriction | Open |
| Subject Keyword | Book Name: A First Graduate Course in Abstract Algebra History and Philosophy of Science Finite Group Maximal Suppose Theorems Isomorphic Obvious |
| Content Type | Text |
| Resource Type | Chapter |
