subgroups with coprime orders
Proof. Let and be such subgroups and and their orders. Then the intersection is a subgroup of both and . By Lagrange’s theorem, divides both and and consequently it divides also which is 1. Therefore , whence the intersection contains only the identity element.
Example. All subgroups
of order 2 of the symmetric group have only the identity element common with the sole subgroup
of order 3.
|Title||subgroups with coprime orders|
|Date of creation||2013-03-22 18:55:58|
|Last modified on||2013-03-22 18:55:58|
|Last modified by||pahio (2872)|