Algebra and abstract structures · Maths EE idea · Solid

Latin squares and group tables

A research question to start from

Which Latin squares are the multiplication tables of groups, and how can this be tested?

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Why it works as a maths EE

A clean question linking combinatorics and algebra, with a test you can design and justify.

Mathematics you would need

Latin squares
Group axioms
Associativity checking
Isomorphism

Much of this goes beyond the DP course. That is expected in a maths EE, but you must understand and explain everything you use.

One possible line of attack

Show every group table is a Latin square.
Find small Latin squares that fail associativity.
Design a test for when a Latin square is a group table and prove it is correct.
Count group tables among Latin squares of order 4.

Scope and difficulty

Solid. Solid.

Pitfalls

Confusing isotopy with isomorphism.
Counting without method.

Where to start reading

Search a library catalogue or a university's open lecture notes for: Latin square group Cayley table associativity test; quasigroups. Prefer textbooks, lecture notes and journal articles to a single website, and cite everything you use (how to reference a maths EE).

Make it your EE

Plan this EEOpens the free EE planner with this question as a starting point. Sharpen the questionSix quick checks for a focused research question. Self-check a draftCheck a section against each criterion, free.