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Everything about Divisible group
Abelian group in which every element can, in some sense, be divided by positive integers
In mathematics, specifically in the field of group theory, a divisible group is an abelian group in which every element can, in some sense, be divided by positive integers, or more accurately, every element is an nth multiple for each positive integer n. Divisible groups are important in understanding the structure of abelian groups, especially because they are the injective abelian groups. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Divisible groupA 5-minute orientation
- Skim a recent paper: Group divisible designs with block size 4 and group sizes 2 and 5Influential work since 2022
- Pick up a classic book: Touching from a DistanceThe most-reprinted book on the subject
- Read the landmark paper: Group divisible designs with block-size fourCited 134 times
- Go sideways: Tor functorA closely related topic
- Go sideways: Category of abelian groupsA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🏆 Landmark papers (most cited)
Group divisible designs with block-size four
An application of modified group divisible designs
Robustness group divisible designs
A Generalization of Group Divisible Designs
Some new group divisible designs
Some families of group divisible designs
Group-divisible rotatable designs
To Quotient Divisible Group Theory. I
🆕 Influential since 2022
Group divisible designs with block size 4 and group sizes 2 and 5
Group divisible designs with block size 4 where the group sizes are congruent to 2 mod 3
A generalization of group divisible t $t$‐designs
Clifford group is not a semidirect product in dimensions N divisible by four
Algebraic constructions of group divisible designs
📚 Books worth reading
Touching from a DistanceDeborah Curtis · 1995
Changing Sexualities and Parental Functions in the Twenty-First CenturyCandida Se Holovko, Frances Thomson-Salo · 2017
Skew linear groupsM. Shirvani · 1986- 📕An Ideal for LivingMark Johnson · 1984
This searing light, the sun and everything else : Joy DivisionJon Savage · 2019
From Joy Division to New OrderMick Middles · 1996
24 hour party peopleAnthony H. Wilson · 2002
Rip it up and start againSimon Reynolds · 2005
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Tor functor In mathematics, the Tor functors are the derived functors of the tensor product of modules over a ring. Along with the Ext functor, Tor is one of the central…
- Category of abelian groups In mathematics, the category A b {\displaystyle \mathbf {Ab} } has the abelian groups as objects and group homomorphisms as morphisms. This is the prototype…
- Endomorphism ring In mathematics, the endomorphisms of an abelian group X form a ring. This ring is called the endomorphism ring of X, denoted by End(X); the set of all…
- Direct sum In mathematics, more specifically in algebra, the direct sum of a collection of abelian groups is an abelian group constructed by combining the given groups…
- Slender group In mathematics, a slender group is a torsion-free abelian group that is "small" in a sense that is made precise in the definition below. Let Z N {\displaystyle…
- Group cohomology In mathematics (more specifically, in homological algebra), group cohomology is a set of mathematical tools used to study groups using cohomology theory…
- Cotorsion group In abelian group theory, an abelian group is said to be cotorsion if any extension of it by a torsion-free abelian group splits. If the group is M {\displaystyl…
- Torsion subgroup In the theory of abelian groups, the torsion subgroup A T {\displaystyle A_{T}} of an abelian group A {\displaystyle A} is the subgroup of A {\displaystyle…