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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Spring 2020 • Question 2

Question

Math 6310 • Algebra Spring 2020 • Question 2

Suppose \((G,+)\) is a finite Abelian group of order \(3^3\cdot 2^3\). Suppose that \(6\cdot G=\{6x\mid x\in G\}\) has 6 elements. Classify \(G\) as a direct sum of cyclic groups.

Raw LaTeX

Suppose \((G,+)\) is a finite Abelian group of order \(3^3\cdot 2^3\). Suppose that
\(6\cdot G=\{6x\mid x\in G\}\) has 6 elements. Classify \(G\) as a direct sum of cyclic groups.

Topic Tags

Abelian Groups and Classification of Finite Abelian Groups Abelian Groups and Direct Sum Decompositions Classification of Finite Groups Finite Group Theory