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17 relations: Abelian group, Academic Press, Brauer–Suzuki theorem, Center (group theory), Centralizer and normalizer, Commutator, Compact group, Conjugacy class, Core (group theory), Finite group, Involution (mathematics), Journal of Algebra, Mathematische Annalen, Normal subgroup, Order (group theory), Sylow theorems, 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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Academic Press
Academic Press is an academic book publisher.
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Brauer–Suzuki theorem
In mathematics, the Brauer–Suzuki theorem, proved by,,, states that if a finite group has a generalized quaternion Sylow 2-subgroup and no non-trivial normal subgroups of odd order, then the group has a centre of order 2.
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Center (group theory)
In abstract algebra, the center of a group,, is the set of elements that commute with every element of.
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Centralizer and normalizer
In mathematics, especially group theory, the centralizer (also called commutant) of a subset S of a group G is the set of elements of G that commute with each element of S, and the normalizer of S are elements that satisfy a weaker condition.
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Commutator
In mathematics, the commutator gives an indication of the extent to which a certain binary operation fails to be commutative.
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Compact group
In mathematics, a compact (topological) group is a topological group whose topology is compact.
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Conjugacy class
In mathematics, especially group theory, the elements of any group may be partitioned into conjugacy classes; members of the same conjugacy class share many properties, and study of conjugacy classes of non-abelian groups reveals many important features of their structure.
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Core (group theory)
In group theory, a branch of mathematics, a core is any of certain special normal subgroups of a group.
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Finite group
In abstract algebra, a finite group is a mathematical group with a finite number of elements.
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Involution (mathematics)
In mathematics, an involution, or an involutory function, is a function that is its own inverse, for all in the domain of.
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Journal of Algebra
Journal of Algebra (ISSN 0021-8693) is an international mathematical research journal in algebra.
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Mathematische Annalen
Mathematische Annalen (abbreviated as Math. Ann. or, formerly, Math. Annal.) is a German mathematical research journal founded in 1868 by Alfred Clebsch and Carl Neumann.
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Normal subgroup
In abstract algebra, a normal subgroup is a subgroup which is invariant under conjugation by members of the group of which it is a part.
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Order (group theory)
In group theory, a branch of mathematics, the term order is used in two unrelated senses.
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Sylow theorems
In mathematics, specifically in the field of finite group theory, the Sylow theorems are a collection of theorems named after the Norwegian mathematician Ludwig Sylow (1872) that give detailed information about the number of subgroups of fixed order that a given finite group contains.
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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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