I'm trying to get a deeper understanding of the classification problem for finite groups and in particular the extension problem. I'm looking for some advanced books on the theory of finite group extensions which extensively and deeply covers the topic. Maybe an all-in-one book doesn't exist, in case I'd like also suggestions on books covering related and more specific topics such as Shur's multiplier and Group cohomology.
2026-03-25 19:02:49.1774465369
Best books on finite group extensions
178 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in GROUP-THEORY
- What is the intersection of the vertices of a face of a simplicial complex?
- Group with order $pq$ has subgroups of order $p$ and $q$
- How to construct a group whose "size" grows between polynomially and exponentially.
- Conjugacy class formula
- $G$ abelian when $Z(G)$ is a proper subset of $G$?
- A group of order 189 is not simple
- Minimal dimension needed for linearization of group action
- For a $G$ a finite subgroup of $\mathbb{GL}_2(\mathbb{R})$ of rank $3$, show that $f^2 = \textrm{Id}$ for all $f \in G$
- subgroups that contain a normal subgroup is also normal
- Could anyone give an **example** that a problem that can be solved by creating a new group?
Related Questions in REFERENCE-REQUEST
- Best book to study Lie group theory
- Alternative definition for characteristic foliation of a surface
- Transition from theory of PDEs to applied analysis and industrial problems and models with PDEs
- Random variables in integrals, how to analyze?
- Abstract Algebra Preparation
- Definition of matrix valued smooth function
- CLT for Martingales
- Almost locality of cubic spline interpolation
- Identify sequences from OEIS or the literature, or find examples of odd integers $n\geq 1$ satisfying these equations related to odd perfect numbers
- property of Lebesgue measure involving small intervals
Related Questions in HOMOLOGY-COHOMOLOGY
- Are these cycles boundaries?
- Cohomology groups of a torus minus a finite number of disjoint open disks
- $f$ - odd implies $d(f)$ - odd, question to the proof
- Poincarè duals in complex projective space and homotopy
- understanding proof of excision theorem
- proof of excision theorem: commutativity of a diagram
- exact sequence of reduced homology groups
- Doubts about computation of the homology of $\Bbb RP^2$ in Vick's *Homology Theory*
- the quotien space of $ S^1\times S^1$
- Rational points on conics over fields of dimension 1
Related Questions in GROUP-COHOMOLOGY
- Group cohomology of $\mathrm{GL}(V)$
- How to compute group cohomology $H^2_\sigma(\mathbb{Z}\times \mathbb{Z}, \mathbb{Z}_2\times \mathbb{Z}_2)$ with nontrivial $G$-module
- Cohomological Interpretation of Modular Forms on a Modular Curve
- Group cohomology with the coefficient $\frac{1}{n}\mathbb{Z}/\mathbb{Z}$
- A $G$-module admits a surjection from a $G$-module, which is free as an abelian group, such that the kernel is free
- Different constructions of group homology
- What is the pushout of $D^n \longleftarrow S^{n-1} \longrightarrow D^n$?
- Group theoretic interpretation of the cohomology of $K(G, n)$
- Action of a group on set of morphisms
- Crossed homomorphism/derivation on free group
Related Questions in GROUP-EXTENSIONS
- Non-split central extension of Z by a finite simple non-abelian group
- Proof of the Schur–Zassenhaus theorem without using homological algebra?
- Generated a non-Abelian group from a Lie group and nontrivial $\mathbb{Z}_2$ action
- Determine possible $p$-groups from center and quotient
- Baer sum of two extensions
- Algorithms to determine the explicit forms of possible group extensions
- How to compute sheaf cohomology of a classifying space?
- Finding whether an extension is normal
- Candidate for showing extension is simple
- Can someone check If this extension is correct?
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?