Let G be an Abelian group. show that the set of all elements of G of finite order forms a subgroup of G.
Prove or disprove, If G is a group in which every proper subgroup is cyclic, then G is cyclic.
show that a abelian group must have five distinct elements
Show that {(1), (1,2)(3,4), (1,3)(2,4), (1,4)(2,3)} is a subgroup of S4 (Ssub4)
Let G = GLsub2 (R). a) show that T = {[a b] ad not equal to 0} is a subgroup of G {[0 d] } b) Show that D = {[a 0] ad not equal to 0} is a subgroup of G {[0 d]
Let G be an abelian group such that the operation on G is denoted additively. Show that {a is an element of G| 2a = 0} is a subgroup of G. Compute the subgroup for G =Z sub 12
Group Equivalence Relation : alpha, beta, sigma
For alpha, beta an element in S sub n, let alpha~ beta if there exists sigma is an element of S sub n such that sigma alpha sigma inverse = beta. Show that ~ is an equivalence relation on S sub n.
Defining a group using axioms.
Define * on Z by a * b = max{a,b}. Is Z a group?
Defining a group using axioms.
Define * on Z by a * b = labl
Defining a group using axioms.
Define * on Q by a * b = ab
