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Ch. 3 Finite Groups and Subgroups
Fichas del conjunto (9)
- 1Define: Order of a GroupThe number of elements of a group is called its order, or |G|.
- 2Order of an elementThe order of an element g in a group G is the smallest positive integer n such that g^n = e. If no such integer exists, then g as infinite order, or |g| = infinity
- 3SubgroupIf a subset H of a group is itself a group under the operation of g, we say that H is a subgroup of G.
- 4One-Step Subgroup TestConsider H, a nonempty subset of G. If ab^(-1) is in H for every a,b in H, then H is a subgroup of G.
- 5Two-Step Subgroup TestConsider H, a nonempty subset of G. If:
1.) every element of H has an inverse, and
2.) ab is in H for every a,b in H
then H is a subgroup of G - 6Finite Subgroup TestLet H be a nonempty finite subset of a group G. If H is closed under operation G, then H is a subgroup of G.
- 7is a subgroupLet G be a group, and let a be any element of G. Then is a subgroup of G.
- 8Define: Center of a GroupThe center, Z(G), of a group G is the subset of elements in G that commute with every element of G.
The center is a subgroup of G. - 9Define: CentralizerLet a be a fixed element of a group G. The centralizer of a in G, C(a), is the set of all elements in G that commute with a.
C(a) is a subgroup of G.
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- (Abstract Algebra) Mathematics Fichas sobre Ch. 3 Finite Groups and Subgroups, creado por William Hartemink el 09/04/2017.
- Creado por
- William Hartemink
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