Order (group theory)
Wikimedia article covering multiple topics
In mathematics, the order of a finite group is the number of its elements. If a group is not finite, one says that its order is infinite. The order of an element of a group (also called period length or period) is the order of the subgroup generated by the element.
Nº Q589491 ★★
Uncommon · Literature
Order (group theory)
Wikimedia article covering multiple topics
In mathematics, the order of a finite group is the number of its elements. If a group is not finite, one says that its order is infinite. The order of an element of a group (also called period length or period) is the order of the subgroup generated by the element.
Last price
—
Floor price
—
7-day median
—
30-day sales
0
30-day range
—
In circulation
0
Price history
median
low – high
sales
No sales in this period
Show table
| Date | median | Low | High | sales |
|---|
Sales history
- Last sale
- —
- 30-day average
- —
- 30-day low
- —
- 30-day high
- —
- Sales 7d
- 0
- Sales 30d
- 0
No sales yet.
Anonymous sales: no buyer or seller shown. Figures count player-to-player sales only.
From Wikipedia
In mathematics, the order of a finite group is the number of its elements. If a group is not finite, one says that its order is infinite. The order of an element of a group (also called period length or period) is the order of the subgroup generated by the element. If the group operation is denoted as a multiplication, the order of an element a of a group, is thus the smallest positive integer m such that am = e, where e denotes the identity element of the group, and am denotes the product of m copies of a. If no such m exists, the order of a is infinite. The order of a group G is denoted by ord(G) or |G|, and the order of an element a is denoted by ord(a) or |a|, instead of ord ( ⟨ a ⟩ ) , {\displaystyle \operatorname {ord} (\langle a\rangle ),} where the brackets denote the generated group. Lagrange's theorem states that for any subgroup H of a finite group G, the order of the subgroup divides the order of the group; that is, |H| is a divisor of |G|. In particular, the order |a| of any element is a divisor of |G|.
Text: Wikipédia, CC BY-SA 4.0. · Image: Original: Jakob.scholbach Vector: Pbroks13 (CC BY-SA 3.0) ·
Related cards
Symmetric group
Group of bijective automorphisms of a set, also called bijective group: the group of bijections on a set (the group of all its permutations), whose group operation is function composition
Nº Q849512 ★★
Ordinal number
Mathematical concept generalizing ordinal numerals to extend enumeration to infinite sets
Nº Q191780 ★★★
Well-ordering principle
Statement that all sets of positive numbers contains a least element
Nº Q2488476 ★★★
Supremum
When it exists, the least element of a partially ordered set which is greater than or equal to all elements of a given subset
Nº Q215071 ★
Maximal and minimal elements
Elements of partially ordered sets such that there is not greater and smaller than each other element, respectively (but there can be incomparable elements)
Nº Q1475294 ★
Lexicographic order
Generalization of the way the alphabetical order of words is based on the alphabetical order of their component letters
Nº Q1144915 ★★★