section of a group
A section of a group is a quotient (http://planetmath.org/QuotientGroup) of a subgroup of . That is, a section of is a group of the form , where is a subgroup of , and is a normal subgroup of .
A group is said to be involved in a group if is isomorphic to a section of .
The relation ‘is involved in’ is transitive (http://planetmath.org/Transitive3), that is, if is involved in and is involved in , then is involved in .
Intuitively, ‘ is involved in ’ means that all of the structure of can be found inside .
Title | section of a group |
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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 |