section of a group

A sectionPlanetmathPlanetmath of a group G is a quotientPlanetmathPlanetmath ( of a subgroupMathworldPlanetmathPlanetmath of G. That is, a section of G is a group of the form H/N, where H is a subgroup of G, and N is a normal subgroupMathworldPlanetmath of H.

A group G is said to be involved in a group K if G is isomorphicPlanetmathPlanetmathPlanetmath to a section of K.

The relationMathworldPlanetmathPlanetmath ‘is involved in’ is transitiveMathworldPlanetmathPlanetmathPlanetmathPlanetmathPlanetmath (, that is, if G is involved in K and K is involved in L, then G is involved in L.

Intuitively, ‘G is involved in K’ means that all of the structureMathworldPlanetmath of G can be found inside K.

Title section of a group
Canonical name SectionOfAGroup
Date of creation 2013-03-22 17:15:04
Last modified on 2013-03-22 17:15:04
Owner yark (2760)
Last modified by yark (2760)
Numerical id 11
Author yark (2760)
Entry type Definition
Classification msc 20F99
Synonym section
Synonym quotient of a subgroup
Defines involved in