Group Theory : Cayley Tables, Cyclic Groups and Isomorphisms

Related BrainMass Solutions

• Isomorphisms, Cyclic Groups and Groups of Permutations

  107387 Isomorphisms, Cyclic Groups and Groups of Permutations Consider the group Z[4] × Z[6] under * such that (a, b) * (c, d) = (a +[4] c, b +[6] d).

• Abstract algebra proofs

  Solution is attached This is a set of abstract algebra problems, involving proofs, sets, groups, a Cayley table, and subgroups.

• Isomorphisms, Residue Classes and Multiplication Tables

  108494 Isomorphisms, Residue Classes and Multiplication Tables Show that U(10) is isomorphic to Z_4 and write out the isomorphism explicitly.

• Symmetric groups and Permutation groups

  (a) Explain why this group has cyclic subgroups of order 1,2,3,4,5 and 6 and give examples of each of these. Explain why this group does not have cyclic subgroups of any order.

• Abstract algebraic operations

  Construct a Cayley Table and show that this set of movements forms a group.

• Isomorphism

  This is a proof regarding isomorphisms and infinite cyclic groups.

• Many problems on group theory

  Draw cayley tables for each one of them( the element should be named a,b,c,d,e) is either (or both) of the groups of order four subgroup of any of those of order five?

• Normal subgroups, Second Theorem of Isomorphism, Conjugates and Cyclic Groups

  96577 Normal subgroups, Second Theorem of Isomorphism, Conjugates and Cyclic Groups Problem 1.

• Direct Products of Groups, Conjugate Subgroups, Homomorphisms and Isomorphisms

  100792 Direct Products of Groups, Conjugate Subgroups, Homomorphisms and Isomorphisms Assume that K is a cyclic group, H is an arbitrary group and f1 and f2 are homomorphisms from K into Aut(H) such that f1(K) and f2(K) are conjugate subgroups of Aut