CRC Concise Encyclopedia of MathematicsUpon publication, the first edition of the CRC Concise Encyclopedia of Mathematics received overwhelming accolades for its unparalleled scope, readability, and utility. It soon took its place among the top selling books in the history of Chapman & Hall/CRC, and its popularity continues unabated. Yet also unabated has been the d |
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Page 18
... mathematical CATEGORY which displays some of the characteristic properties of the CATEGORY of all ABELIAN GROUPS . See also ABELIAN GROUP , CATEGORY The KRONECKER DECOMPOSITION THEOREM states that every FINITE Abelian group.
... mathematical CATEGORY which displays some of the characteristic properties of the CATEGORY of all ABELIAN GROUPS . See also ABELIAN GROUP , CATEGORY The KRONECKER DECOMPOSITION THEOREM states that every FINITE Abelian group.
Page 19
... group can be written as a GROUP DIRECT PRODUCT of CYCLIC GROUPS of PRIME POWER ORDER . If the ORDER of a FINITE GROUP is a PRIME P , then there exists a single Abelian group of order p ( denoted Z , ) and no non - Abelian groups . If ...
... group can be written as a GROUP DIRECT PRODUCT of CYCLIC GROUPS of PRIME POWER ORDER . If the ORDER of a FINITE GROUP is a PRIME P , then there exists a single Abelian group of order p ( denoted Z , ) and no non - Abelian groups . If ...
Page 20
... groups are not ABELIAN . However, there is always a GROUP HOMOMORPHISM h : G 0 G? to an ABELIAN GROUP , and this homomorphism is called Abelianization. The homomorphism is abstractly described by its kernel, the COMMUTATOR SUBGROUP [G ...
... groups are not ABELIAN . However, there is always a GROUP HOMOMORPHISM h : G 0 G? to an ABELIAN GROUP , and this homomorphism is called Abelianization. The homomorphism is abstractly described by its kernel, the COMMUTATOR SUBGROUP [G ...
Page 35
... GROUP , AFFINE HULL , AFFINE PLANE , AFFINE SPACE , AFFINE TRANSFORMA- TION , AFFINITY , COMPLEX PLANE , COMPLEX PROJEC- TIVE PLANE Affine Connection CONNECTION COEFFICIENT Affine Equation A nonhomogeneous LINEAR EQUATION or system of ...
... GROUP , AFFINE HULL , AFFINE PLANE , AFFINE SPACE , AFFINE TRANSFORMA- TION , AFFINITY , COMPLEX PLANE , COMPLEX PROJEC- TIVE PLANE Affine Connection CONNECTION COEFFICIENT Affine Equation A nonhomogeneous LINEAR EQUATION or system of ...
Page 61
... groups An for n = 2 , 3 , are 1 , 3 , 4 , 5 , 7 , 9 , ... ( Sloane's A000702 ) . See also 15 PUZZLE , FINITE GROUP , GROUP , JORDAN'S SYMMETRIC GROUP THEOREM , LIE GROUP , PERMUTA- TION GROUP , SIMPLE GROUP , SYMMETRIC GROUP References ...
... groups An for n = 2 , 3 , are 1 , 3 , 4 , 5 , 7 , 9 , ... ( Sloane's A000702 ) . See also 15 PUZZLE , FINITE GROUP , GROUP , JORDAN'S SYMMETRIC GROUP THEOREM , LIE GROUP , PERMUTA- TION GROUP , SIMPLE GROUP , SYMMETRIC GROUP References ...
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Common terms and phrases
Abramowitz Academic Press Addison-Wesley Algebraic ALGORITHM Amer ANGLE ARCHIMEDEAN SOLID Arfken AXIOM Bernoulli BESSEL FUNCTION BETA FUNCTION BINOMIAL COEFFICIENT Boca Raton BROCARD Calculus called Cambridge University Press CIRCLE Combinatorics COMPLEX NUMBER Comput CONIC Conjecture constant Continued Fractions Convex COORDINATES Coxeter CRC Press CUBE Cubic curve CYCLOID defined denoted Dictionary of Curious Differential Equations Differential Geometry digits Diophantine Equation Dirichlet Discrete Mathematics DISTRIBUTION DIVISOR DIVISOR FUNCTION Dover Encyclopedia of Integer England ffiffiffi finite FORMULA Geometry given Graph Theory GROUP HYPERGEOMETRIC identity Integer Sequences intersection JOHNSON SOLID KNOT Math Mathematica Mathematical Tables MATRIX N. J. A. Sequences Number Theory On-Line Version Penguin Dictionary PLANE points POLYGON POLYHEDRON POLYNOMIAL POLYOMINO PRIME Problem References RIEMANN ZETA FUNCTION SERIES Skiena Sloane Sloane's solution SPACE Springer-Verlag SQUARE Stegun SURFACE TANGENT THEOREM TION Topology TRANSFORM TRIANGLE VECTOR Weisstein Wiley York