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Height (abelian group)

In mathematics, the height of an element g of an abelian group A is an invariant that captures its divisibility properties: it is the largest natural number N such that the equation Nx = g has a solution x ∈ A, or the symbol ∞ if there is no such N. The p-height considers only divisibility properties by the powers of a fixed prime number p. The notion of…

Measurement, Ulm's theorem & Definition of height

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Definition of height

Ulm subgroups

Ulm's theorem

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Height (abelian group)

Nodes29
Edges28
Triples0
Avg. degree1.93
Density0.068966
Components1

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ulm height abelian theorem group ordinal number ulm's infinite groups p-height subgroup elements factors subgroups pαa filtration uσ countable largest

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