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Group-군

저작시기 2006.09 |등록일 2006.12.22 한글파일한글 (hwp) | 15페이지 | 가격 2,000원

소개글

현대대수, 대수학 군(group) 에 관한 논문입니다.
수학과 논문.

목차

1. groups
2. subgroup
3. cyclic groups
4. homomorphism
5. normal subgroups
6. factor groups

본문내용

1. Groups

Definition (Group)
A group < *> is a set , closed under a binary operation *, such that the following axiom are satisfied:
: For all , we have
****. associativity of *
: There is an element in such that for all
.
**. identity element for *
: Corresponding to each , there is an
element in such that
**. inverse of

Definition
A group is abelian if its binary operation is commutative.

Example
The set Z+ under multiplication is not group. There is an identity 1, but no inverse of 3.

Example
The set of all real-valued functions with domain R under function addition is a group. This group is abelian.

Example
The set Mm×n(R) of all m×n matrices under matrix addition is a group. The m×n matrix with all entries 0 is the identity matrix. This group is abelian.

Theorem
In group with binary operation *, there is only one element in such that
**
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