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P-group

In mathematics, specifically group theory, given a prime number p, a p-group is a group in which the order of every element is a power of p. That is, for each element g of a p-group G, there exists a nonnegative integer n such that the product of pn copies of g, and not fewer, is equal to the identity element. The orders of different elements may be…

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Application to structure of a group

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P-group

Nodes91
Edges90
Triples66
Avg. degree1.98
Density0.021978
Components1

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P-group

Top relations

related to Iterated wreath products · 9
P-group → Denote, GL, It, Maximal, Since, Sylow, Sym, The, Then
related to Properties · 8
P-group → Being, Cauchy's, Correspondence Theorem, Every, G/H, If, This, We
related to Classification · 7
P-group → For, James, Marshall Hall Jr, Philip Hall, Rather, Senior, The
related to Generalized dihedral groups · 7
P-group → Form, However, Let, Pn, The, There, When
related to Automorphisms · 6
P-group → Burnside, Every, Frattini, G/Φ, Just, The
related to Examples · 6
P-group → C4, Dih4, However, Klein, Nor, V4
related to External links · 6
P-group → Eric, Group, MathWorld, Rowland, Todd, Weisstein
related to Within a group · 5
P-group → Cauchy's, Every, In, Sylow, This
related to Application to structure of a group · 3
P-group → As, Sylow, These
is a · 2
P-group → group in which the order of every element is a power of p, subgroup of the center consisting of the central elements of order p.If G is a p-group

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Important terminology

order group groups finite subgroup every p-groups abelian pn center sylow dihedral subgroups cyclic also non-trivial normal class example elements

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
P-groupis agroup in which the order of every element is a power of p0.90text
P-groupis asubgroup of the center consisting of the central elements of order p.If G is a p-group0.90text
the focal subgroup theoreminstance ofpossess important properties0.80text
and allow one to determine many aspects of the structure of the group.Local controlMuch of the structure of a finite group is carried in the structure of its so-called local subgroupsinstance ofpossess important properties0.80text
the normalizers of non-identity p-subgroups.The large elementary abelian subgroups of a finite group exert control over the group that was used in the proof of the Feitinstance ofpossess important properties0.80text
P-grouprelated to Application to structure of a groupAs0.60section
P-grouprelated to Application to structure of a groupSylow0.60section
P-grouprelated to Application to structure of a groupThese0.60section
P-grouprelated to AutomorphismsThe0.60section
P-grouprelated to AutomorphismsJust0.60section
P-grouprelated to AutomorphismsEvery0.60section
P-grouprelated to AutomorphismsG/Φ0.60section

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