section of a group

A section of a group $G$ isa quotient (http://planetmath.org/QuotientGroup) 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 (http://planetmath.org/Transitive3),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 $K$ .

单词	SectionOfAGroup
释义	section of a group A section of a group $G$ isa quotient (http://planetmath.org/QuotientGroup) 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 (http://planetmath.org/Transitive3),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 $K$ .
随便看	positive multiple of a semiperfect number is also semiperfect PositiveRoot positive root PositiveSemidefinite positive semidefinite positive semidefinite PositiveSemidefinite1 PositivityInOrderedRing positivity in ordered ring PossibleOrdersOfEllipticFunctions possible orders of elliptic functions PostCorrespondenceProblem Post correspondence problem PostSystem Post system PotentialOfHollowBall potential of hollow ball PotentialTheory potential theory PouletNumber Poulet number PowerassociativeAlgebra power-associative algebra PowerBasisOvermathbbZ power basis over ℤ