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section of a group (Definition)

A section of a group $G$ is a quotient of a subgroup 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 subgroup of $H$.

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

The relation `is involved in' is transitive, 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 structure of $G$ can be found inside $K$.



"section of a group" is owned by yark.
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Other names:  section, quotient of a subgroup
Also defines:  involved in
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Cross-references: isomorphic, normal subgroup, subgroup, group
There are 4 references to this entry.

This is version 8 of section of a group, born on 2007-06-13, modified 2007-06-15.
Object id is 9584, canonical name is SectionOfAGroup.
Accessed 1145 times total.

Classification:
AMS MSC: 20F99 (Group theory and generalizations :: Special aspects of infinite or finite groups :: Miscellaneous)
Pending Errata and Addenda
None.
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