About: Descendant tree (group theory)

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In mathematics, specifically group theory, a descendant tree is a hierarchical structure that visualizes parent-descendant relations between isomorphism classes of finite groups of prime power order , for a fixed prime number and varying integer exponents . Such groups are briefly called finite p-groups. The vertices of a descendant tree are isomorphism classes of finite p-groups.

Attributes	Values
rdfs:label	Descendant tree (group theory) (en)
rdfs:comment	In mathematics, specifically group theory, a descendant tree is a hierarchical structure that visualizes parent-descendant relations between isomorphism classes of finite groups of prime power order , for a fixed prime number and varying integer exponents . Such groups are briefly called finite p-groups. The vertices of a descendant tree are isomorphism classes of finite p-groups. (en)
sameAs	Descendant tree (group theory) Descendant tree (group theory)
dbp:wikiPageUsesTemplate	dbt:Hidden_begin dbt:Hidden_end dbt:Reflist dbt:EquationNote
Subject	P-groups Subgroup series Topological groups Trees (data structures) Group theory
thumbnail	wiki-commons:Special:FilePath/Terminology_of_trees.png?width=300
foaf:depiction
prov:wasDerivedFrom	http://en.wikipedia.org/wiki/Descendant_tree_(group_theory)?oldid=1043708899&ns=0
Wikipage page ID	42823620 (xsd:integer)
page length (characters) of wiki page	48812 (xsd:nonNegativeInteger)
Wikipage revision ID	1043708899 (xsd:integer)
Link from a Wikipage to another Wikipage	Magma (computer algebra system) Normal subgroup Pro-p group Algebra Artin transfer (group theory) P-groups Subgroup series Topological groups Trees (data structures) Central series Giuseppe Bagnera (mathematician) Group theory P-group P-group generation algorithm Serial module Presentation of a group Cohomology Commutator subgroup Space group GAP (computer algebra system) Descendant tree (group theory) Group theory Tree (graph theory) Tree (set theory) Tree structure Topological group Isomorphism class Numerical analysis Nilpotent group Quotient group
has abstract	In mathematics, specifically group theory, a descendant tree is a hierarchical structure that visualizes parent-descendant relations between isomorphism classes of finite groups of prime power order , for a fixed prime number and varying integer exponents . Such groups are briefly called finite p-groups. The vertices of a descendant tree are isomorphism classes of finite p-groups. Additionally to their order , finite p-groups have two further related invariants, the nilpotency class and the coclass . It turned out that descendant trees of a particular kind, the so-called pruned coclass trees whose infinitely many vertices share a common coclass , reveal a repeating finite pattern. These two crucial properties of finiteness and periodicity admit a characterization of all members of the tree by finitely many parametrized presentations. Consequently, descendant trees play a fundamental role in the classification of finite p-groups. By means of kernels and targets of Artin transfer homomorphisms, descendant trees can be endowed with additional structure. An important question is how the descendant tree can actually be constructed for an assigned starting group which is taken as the root of the tree. The p-group generation algorithm is a recursive process for constructing the descendant tree of a given finite p-group playing the role of the tree root. This algorithm is implemented in the computational algebra systems GAP and Magma. (en)
foaf:isPrimaryTopicOf	http://en.wikipedia.org/wiki/Descendant_tree_(group_theory)
is Link from a Wikipage to another Wikipage of	Artin transfer (group theory) Central series Giuseppe Bagnera (mathematician) Coclass Descendant tree (group theory) Mihály Nagy
is foaf:primaryTopic of	http://en.wikipedia.org/wiki/Descendant_tree_(group_theory)

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