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Everything about Normal subgroup
Subgroup invariant under conjugation
In abstract algebra, a normal subgroup is a subgroup that is invariant under conjugation by members of the group of which it is a part. In other words, a subgroup of the group is normal in if and only if for all and The usual notation for this relation is Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Normal subgroupA 5-minute orientation
- Skim a recent paper: The average character degree and r-solvability of a normal subgroupInfluential work since 2022
- Pick up a classic book: A first course in abstract algebraThe most-reprinted book on the subject
- Read the landmark paper: COMPLEX INTUITIONISTIC FUZZY NORMAL SUBGROUPCited 24 times
- Go sideways: Kernel (algebra)A closely related topic
- Go sideways: Quotient groupA closely related topic
📖 Definitions
Noun A subgroup H of a group G that is invariant under conjugation; that is, for all elements h of H and for all elements g in G, the element ghg is in H.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
COMPLEX INTUITIONISTIC FUZZY NORMAL SUBGROUP
Finite Permutation Groups with a Transitive Minimal Normal Subgroup
Conjugacy Classes Outside a Normal Subgroup
Normal subgroup generated by a plane polynomial automorphism
The normal subgroup structure of the Picard group
On groups with every normal subgroup transitive or semiregular
The fuzzy normal subgroup
$L$-Fuzzy Subgroup Degrees and $L$-Fuzzy Normal Subgroup Degrees
🆕 Influential since 2022
The average character degree and r-solvability of a normal subgroup
Groups Having all Elements off a Normal Subgroup with Prime Power Order
Genus and crosscap of normal subgroup based power graphs of finite groups
On the Separability of Abelian Subgroups of the Generalized Free Product of Two Groups with Normal Amalgamated Subgroup
On Conjugacy Class Graph of Normal Subgroup
📚 Books worth reading
A first course in abstract algebraJohn B. Fraleigh · 1967
Abstract algebraWilliam Paulsen · 2010
Abstract algebraDavid S. Dummit · 1991- 📕Structural Aspects of Quantum Field Theory and Noncommutative GeometryGerhard Grensing · 2013
- 📕Complementation of Normal SubgroupsJoseph Kirtland · 2017
2000 Solved Problems in Discrete MathematicsSeymour Lipschutz · 1991
Quantum computer scienceMarco Lanzagorta · 2008
DementiaV. Olga B. Emery, Thomas E. Oxman · 2003
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
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