FiniteGroups

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Contents

• AdaptiveMergeRepair
• Abelianization does not characterize right quotient multisets
• Refutation of the peak-group dichotomy
• The original Bajnok–Beatty Conjecture 4.1
• Exact growth and diameter of asymmetric lattice quotients
• Exact first reversal and the complete final pre-wrap band
• An affine odd square detects the necessary congruences
• From actual quotient return words to simple Cayley graph moments
• A skew lattice construction for the even-radius sufficiency direction
• Exact growth from finite rank-one fibers
• Abstract finite noncyclic upper bounds
• The first characteristic coefficient separating the actual Cayley graphs
• First-return defect for the same actual quotients
• The initial odd-wrap return gap at t=2
• A centered-ceiling counterexample for the original return threshold
• A uniform early return gap at the first odd wrap
• A strict finite Gaussian envelope for the original quotient returns
• The Gaussian root, secant, and alpha bounds
• A finite second-order Gaussian envelope for the original returns
• Finite Gaussian upper envelope for the original quotient returns
• A late strict return gap at the first odd wrap
• A sharper negative cone for the original odd-wrap quotients
• A sharper positive cone for the original odd-wrap quotients
• Exact returns at the first odd wrap
• A second-order threshold bracket with an explicit coefficient
• The unique odd-wrap sign threshold
• A finite quantitative bracket for the complete original return threshold
• Same group and diameter, different growth
• The Bajnok–Beatty sharp maximum for radius at least three
• Exact first even return band for the two lattice quotients
• All-q square-displacement correction coefficient
• A uniform square-displacement envelope for actual counts
• The fourth square-displacement coefficient
• A fourth-order envelope for actual square-displacement counts
• One group and exact growth gaps for all odd square displacements
• The log-two threshold bracket
• Square-displacement profiles and coefficient scaling
• The scale of the finite square-displacement remainder
• The all-odd square-displacement threshold
• The corrected threshold bracket for all odd square displacements
• A CRT law for actual square-displacement thresholds
• Perfect restricted bases of size s + 1
• BhanjaRestrictedSumset
• The native Coxeter quotient obstruction
• Normalizer Quotient and Right-Coset Centralizer
• Character Degree Divisibility
• Clifford Constituents
• Clifford Decomposition
• Irreducible representations of products with abelian groups
• Finite Group Obstruction for Orders Nine, Three and Two
• Cyclic Prime-Power Split Extensions
• Finite Character Algebra
• Finite Otto congruence quotients are cancellative
• The Ordinary Frattini Automorphism Kernel
• Central elements and Frobenius complements
• Degrees over an abelian normal subgroup
• Gaschutz Lifting with an Arbitrary Fixed Set
• Reversible mixed-radix carries
• Full-set sequencing in finite abelian groups
• Gordon interleaving and directed differences
• Orientation dependence of greedy involution counts
• HeadleyC2C4OddProduct
• The exhaustive coordinate cases
• Cyclic kernels and the exponent measure
• HeadleyCubeOddProduct
• The doubled-coordinate subgroup and E4 quotient
• Field orbits and the small two-primary leaves
• Headley nonsplit extension
• HeadleyOddProduct
• HeadleyOddRows
• Headley rank-two R-star construction
• Headley rank-two circular-length paths
• R-cycles for all noncyclic finite abelian two-groups
• Abstract finite abelian two-groups in coordinates
• Induced Character Formula
• A missing square point forces a smaller Lee cover
• Consecutive Davenport constants of finite groups
• Mackey Character Formula
• Rigidity from adjacent columns and quotient index
• NikolovSegal
• Exact endpoint count for signed coordinate words
• An intermediate finite-group invariant
• Quandles
• Rational Attainment of Subgroup Conjugacy Ratios
• RegularRepresentation
• Relative Frattini Kernels
• Restricted pair sums and additive stabilizers
• The finite SL2(F5) central-square certificate
• Recognition of Simple Groups of Order Sixty
• Subgroup Conjugacy Ratios
• Root factors of successor cycles
• A canonical quotient of a directed relation
• Tărnăuceanu’s reciprocal subgroup-order conjecture
• Complete Support for Toral Character Triples