PRINT LINKED RELATED

Fundamental Homomorphism Theorem Homework

Directions: Write your homework legibly with a pencil. Complete the homework on time and by yourself. For each problem, write the instructions, label the solution/proof and show all steps. Do not turn in your scratch work. Staple your pages together, with the problems in the correct order, and use this page as a cover sheet with your name at the top right.

(1) Find the homomorphic images of the group

(2) Find the homomorphic images of the group

(3) Find the homomorphic images of the group

(4) Find the homomorphic images of the group

(5) Find two non-isomorphic extensions of by

(6) Find two non-isomorphic extensions of by

(7) Use the Fundamental Homomorphism Theorem to prove that if is any group with identity then

(8) Prove that if is a simple Abelian group, then for some prime

(9) Prove that if and are positive integers and is a divisor of then

(10) (First Isomorphism Theorem) Assume that and are subgroups of a group and

    (a) prove that is a subgroup of and that
    
    (b) Define by for each Verify that is a homomorphism of onto
    
    (c) Verify that Now explain why

(11) (Second Isomorphism Theorem) Assume that and are subgroups of a group and that and Prove that and that

Abstract Algebra Books

Contemporary Abstract Algebra. List Price: $163.95 Buy New: $148.88 You Save: $15.07 (9%) New (1) from $148.88Abstract Algebra, Fifth Edition, includes challenging topics as well as numerous figures, tables, photographs, charts, biographies and computer exercises, making the text more compelling, current, and (more)

A First Course in Abstract Algebra, 7th Edition List Price: $124.00 Buy New: $66.00 You Save: $58.00 (47%) New (30) Used (23) from $66.00This is an in-depth introduction to abstract algebra. Focused on groups, rings and fields, it should give students a firm foundation for more specialized work by emphasizing an understanding of the nature (more)

Abstract Algebra: An Introduction List Price: $195.95 Buy New: $104.99 You Save: $90.96 (46%) New (16) Used (19) from $104.99Abstract Algebra: An Introduction (more)

Abstract Algebra Buy New: $50.00 New (28) Used (28) from $49.98Widely acclaimed algebra text. This book is designed to give the reader insight into the power and beauty that accrues from a rich interplay between different areas of mathematics. The book carefully develops (more)

Abstract Algebra: A First Course List Price: $54.95 Buy New: $43.96 You Save: $10.99 (20%) New (3) Used (1) from $43.96The Second Edition of this classic text maintains the clear exposition, logical organization, and accessible breadth of coverage that have been its hallmarks. It plunges directly into algebraic structures (more)

Schaum's Outline of Modern Abstract Algebra (Schaum's) List Price: $18.95 Buy Used: $4.66 You Save: $14.29 (75%) New (20) Used (27) from $4.66If you want top grades and a thorough understanding of abstract algebra this powerful study tool is the best tutor you can have! It takes you step-by-step through the subject and gives you sample problems (more)

Abstract Algebra, 3rd Edition Buy New: $58.78 New (23) Used (24) from $49.85 (more)

Schaum's Outline of Abstract Algebra (Schaum's Outlines) List Price: $18.95 Buy Used: $4.72 You Save: $14.23 (75%) New (32) Used (21) from $4.72This long-awaited revision provides a concise introduction to topics in abstract algebra, taking full account of the major advances and developments that have occurred over the last half-century in the (more)

Elements of Abstract Algebra List Price: $12.95 Buy New: $7.94 You Save: $5.01 (39%) New (12) Used (12) from $4.30Helpful illustrations and exercises included throughout this lucid coverage of group theory, Galois theory and classical ideal theory stressing proof of important theorems. Includes many historical notes. (more)