Group Theory - Closure and Associativity : To determine whether the system described is a group. G = set of all integers, a.b ≡ a - b

To determine whether the system described is a group. G = set of all integers, a.b ≡ a - b

Group Theory - Closure, Associativity, Identity, Commutativity, Inverse : To determine whether the system described is a group. G = set of all integers, a.b ≡ a - b

To determine whether the system described is a group. G = set of all integers, a.b ≡ a + b

Indecomposable representations of quiver A_n

Classify the indecomposable representations of the quiver A_n with the orientation: o -> o -> o -> ... -> o

Groups

Modern Algebra Group Theory (V) Determine whether the system described is a group. G = set of all positive integers, a.b = ab , the usual product of integers.

Group theory

Modern Algebra Group Theory (VI) To determine whether the system described is a group. G = set of all rational numbers with odd denominators, a.b ≡ a + b, the usual addition of rational numbers.

Abelian groups

Modern Algebra Group Theory (VII) To prove that if G is an abelian group, then for all a,bЄG and all integers n, (a.b)^n=a^n.b^n.

Modern Algebra, Group Theory (VIII): If is a group such that (ab)^2=a^2b^2 for all a,bЄG, show that G must be abelian. Or, Show that the group G is abelian iff (ab)^2=a^2b^2.

Modern Algebra Group Theory (VIII) If G is a group such that (ab)^2=a^2b^2 for all a,bЄG, show that G must be abelian. Or, Show that the group G is abelian iff (ab)^2=a^2b^2.

Abelian group

Modern Algebra Group Theory (IX) If G is a group in which (a.b)^i =a^i.b^i for three consecutive integers i for all a,bЄG , show that G is abelian.

Abelian group

Modern Algebra Group Theory (X) In a group G in which (a.b)^i =a^i.b^i for three consecutive integers for all a,bЄG , then G is abelian. Show that the conclusion does not ...continues

Group Theory - Symmetric Set of Permutations : In S3 give an example of two elements x,y such that (x.y)^2 ≠ x^2.y^2.

In S3 give an example of two elements x,y such that (x.y)^2 ≠ x^2.y^2.