Changelog

Most recent update

June 4, 2025

• Added the problem Centralizers in symmetric groups to the problem bank.

Earlier updates

May 26, 2025

• Removed the problem Existence of an identity element in a group from the Problem Bank. It was similar to, but more awkward than Existence of an identity element in a finite ring.

May 19, 2025

• Removed from the problem bank the following problems, each for being either too tricky, long, or ambiguous:
  • Existence of an identity element in a finite ring
  • Matrix representing a linear transformation
  • Quotients and direct products
  • Image of a normal subgroup and induced morphisms
  • Analyzing an unusual matrix

May 8, 2025

• Fixed a typo in Automorphisms of a finite cyclic group. Previously the definition of the map ${\mu }_m$ was typographically mangled.
• The problem Boolean algebras was removed from the Problem Bank. It is tricky in a way that does not necessarily test understanding of core concepts in ring theory.

April 29, 2025

• Relaxed a condition in the problem Image of the identity is the identity. The original version assumed $\varphi$ was an isomorphism of groups, but the desired result only requires $\varphi$ to be a (homo)morphism.

**April 22, 2025

• Added dates for all exams given since Spring 2022

April 5, 2025

• Updated this problem to remove an incorrect hint. (Previously, the second part of the problem claimed that the kernel of the morphism required two generators, contrary to the fact that $\mathbf{Z}[i]$ is a PID.)

April 4, 2025

• Added this changelog page
• Removed from the Problem Bank all problems referencing Jordan canonical form and/or general inner product spaces. Specifically, the following four problems below were removed from the pool
  • Jordan canonical form of a matrix
  • Jordan canonical form of a matrix (2)
  • Numerical range of a linear transformation
  • Projections and adjoints

March 31, 2025

• Added Notation Key
• Updated typography

March 29, 2025
Initial release, including:

• Exam overview at The Algebra Qual
• Exam syllabus
• Problem bank, consisting of all problems asked on exams between March 2014 and January 2025
• Recreation of all exams between March 2014 and January 2025

Related pages

Home for the Algebra Qual
Exam Syllabus
Notation Key
Problem bank
Past exams