example of groups of order pq
As a specific example, let us classify groups of order 21. Let be a group of order 21. There is only one Sylow 7-subgroup so it is normal. The possibility of there being conjugate Sylow 3-subgroups is not ruled out. Let denote a generator for , and a generator for one of the Sylow 3-subgroups . Then , and for some since is normal. Now , or . This implies , or 4.
Case 2: , then every product of the elements can be reduced to one in the form , , . These 21 elements are clearly distinct, so .
Case 3: , then since is also a generator of and , we have recovered case 2 above.
|Title||example of groups of order pq|
|Date of creation||2013-03-22 14:51:15|
|Last modified on||2013-03-22 14:51:15|
|Last modified by||jh (7326)|