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11 relations: Abelian group, Cyclic group, Finitely generated abelian group, Group (mathematics), Integer, Mathematics, Natural number, P-group, Prüfer group, Prime number, Torsion group.
Abelian group
In abstract algebra, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements does not depend on the order in which they are written.
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Cyclic group
In algebra, a cyclic group or monogenous group is a group that is generated by a single element.
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Finitely generated abelian group
In abstract algebra, an abelian group is called finitely generated if there exist finitely many elements x1,..., xs in G such that every x in G can be written in the form with integers n1,..., ns.
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Group (mathematics)
In mathematics, a group is an algebraic structure consisting of a set of elements equipped with an operation that combines any two elements to form a third element and that satisfies four conditions called the group axioms, namely closure, associativity, identity and invertibility.
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Integer
An integer (from the Latin ''integer'' meaning "whole")Integer 's first literal meaning in Latin is "untouched", from in ("not") plus tangere ("to touch").
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Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
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Natural number
In mathematics, the natural numbers are those used for counting (as in "there are six coins on the table") and ordering (as in "this is the third largest city in the country").
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P-group
In mathematical group theory, given a prime number p, a p-group is a group in which each element has a power of p as its order.
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Prüfer group
In mathematics, specifically in group theory, the Prüfer p-group or the p-quasicyclic group or p∞-group, Z(p∞), for a prime number p is the unique ''p''-group in which every element has p different p-th roots.
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Prime number
A prime number (or a prime) is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers.
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Torsion group
In group theory, a branch of mathematics, a torsion group or a periodic group is a group in which each element has finite order.
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