Linear independence of embeddings
Let E be a finite extension of a field F. Show that any finite set of distinct embeddings of E into the algebraic closure of F is linearly independent over F.
abstract algebra subgroup problem
let G be an abelian group. show that the set of all elements of G of finite order forms a subgroup of G.
proving or disproving a group problem
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)
show a matrice operation is a subgroup of G
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]
reposting a problem because I made a typo in the 2nd art of the ? abelian subgroup
et G be an agelian group such that the operation on G is denoted additively. Show that {a is an element of G| 2a = 0} os a subgroup of G. Compute the subgroup for G =13. The typo is: Compute the subgroup for G =13. It should be Compute the subgroup for G = Z sub 12
group equivalence relation, alpha, beta, sigma
For alpha, beta an element in S sub n, let alph a~ 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 I hope this is understandabe
determining if a group using axioms
define * on Z by a * b = max{a,b}
define * on Z by a * b = labl
