Abstract Algebra One (Practice Exam Two)

(1) Find all subgroups of

(2) Solve the equations: and

(3) Let be a finite group with and identity The order of is defined to be the least positive integral power such that Determine the order of in

(4) Determine the smallest subset of such that and is closed with respect to addition and division.

(5) Let and Both and are subgroups of Show that is not a subgroup of Explain what this means.

(6) Determine the group of symmetries for a square with only one of its diagonals.

(7) Let be a relation on a set Complete each of the following statements.

    (a) The equivalence relation is not reflexive if and only if ___________________.
    
    (b) The equivalence relation is not symmetric if and only if ___________________.
    
    (c) The equivalence relation is not transitive if and only if ___________________.
    

(8) Find a flaw in the following "proof" that a relation on a set is reflexive if it is both symmetric and transitive: Let From by symmetry we have By transitivity, and imply Therefore, is reflexive.

Abstract Algebra Books

Contemporary Abstract Algebra (student solution menual) Buy New: $38.00 New (10) Used (4) from $38.00 (more)

A First Course in Abstract Algebra, 7th Edition List Price: $124.00 Buy Used: $45.00 You Save: $79.00 (64%) New (21) Used (20) from $45.00This 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)

Elements of Abstract Algebra List Price: $12.95 Buy Used: $4.98 You Save: $7.97 (62%) New (19) Used (21) from $4.98Helpful 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)

Abstract Algebra Buy New: $80.79 New (30) Used (21) from $80.79Widely 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: An Introduction List Price: $195.95 Buy New: $72.72 You Save: $123.23 (63%) New (19) Used (22) from $68.50Abstract Algebra: An Introduction (more)

A Book of Abstract Algebra Buy New: $90.00 New (13) Used (6) from $81.13This text is aimed at the abstract or modern algebra course taken by junior and senior math majors and many secondary math education majors. A mid-level approach, this text features clear prose, an intuitive (more)

An Introduction to Abstract Algebra with Notes to the Future Teacher List Price: $125.00 Buy New: $65.99 You Save: $59.01 (47%) New (21) Used (9) from $65.99 This traditional treatment of abstract algebra is designed for the particular needs of the mathematics teacher. Readers must have access to a Computer Algebra System (C. A. S.) such as Maple, or at minimum (more)

A History of Abstract Algebra List Price: $49.95 Buy New: $35.22 You Save: $14.73 (29%) New (30) Used (9) from $35.22Prior to the nineteenth century, algebra meant the study of the solution of polynomial equations. By the twentieth century algebra came to encompass the study of abstract, axiomatic systems such as groups, (more)

Schaum's Outline of Modern Abstract Algebra (Schaum's) List Price: $18.95 Buy Used: $5.38 You Save: $13.57 (72%) New (23) Used (26) from $5.38Confusing Textbooks? Missed Lectures? Not Enough Time? Fortunately for you, there's Schaum's Outlines. More than 40 million students have trusted Schaum's to help them succeed in the classroom and on (more)

• print this page
• pages linking here
• related pages