mth400 | undergraduate

Abstract Algebra I

Explore by:

or call us at



This is the first course of a two-part course sequence presenting students with the applications of abstract algebraic theories. Students will investigate Group theory; including permutation groups, Abelian groups, finite groups, and homomorphism theorems.

This undergraduate-level course is 5 This course is available to take individually or To enroll, speak with an Enrollment Representative.

Course details:

Credits: 3
Continuing education units: XX
Professional development units: XX
Duration: 5

topic title goes here


    • Identify normal subgroups for a given group and quotient groups.
    • Verify relationships between different groups using the Fundamental Homomorphism theorem.
    • Determine if a given mapping is a homomorphism of groups.
    • Find a kernel of a homomorphism.

    Equivalence, Congruence and Divisibility

    • Compute the greatest common divisor and least common multiple of pairs of integers.
    • Verify properties of an equivalence relation.
    • Find representatives of equivalence classes.
    • Identify congruence classes modulo n.
    • Perform the division algorithm.
    • Apply group properties to Zn.
    • Use the Euclidean Algorithm to prove statements involving greatest common divisors.

    Groups: Lagrange’s Theorem and Isomorphism

    • Determine subgroups for a given group and its elements’ order.
    • Identify generators and direct products of groups.
    • Find all subgroups of a given group using Lagrange’s theorem and its corollaries.
    • Determine the cosets of a given group.
    • Determine if given groups are isomorphic.
    • Use Cayley’s theorem to find permutations associated with an element of a group.

    Permutation Groups

    • Apply Sylow’s theorem to calculate Sylow subgroups.
    • Use Burnside’s Counting theorem to determine the number of orbits for a group acting on a set.
    • Determine an action of a finite group on a set.

    Introduction to Groups

    • Determine if a given set, with respect to a given operation, forms a group.
    • Determine properties of permutations.
    • Decide if a given subset is a subgroup.
    • Determine the group of symmetries of a given figure.
    Tuition for individual courses varies. For more information, please call or chat live with an Enrollment Representative.

    Please ask about these special rates:

    Teacher Rate: For some courses, special tuition rates are available for current, certified P-12 teachers and administrators. Please speak with an Enrollment Representative today for more details.

    Military Rate: For some courses, special tuition rates are available for active duty military members and their spouses. Please speak with an Enrollment Representative today for more details.

    The University of Phoenix reserves the right to modify courses.

    While widely available, not all programs are available in all locations or in both online and on-campus formats. Please check with a University Enrollment Representative.

    Transferability of credit is at the discretion of the receiving institution. It is the student’s responsibility to confirm whether or not credits earned at University of Phoenix will be accepted by another institution of the student’s choice.