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Homomorphisms, quotients and the structure of groups · GRE Mathematics Subject Test · Courselo

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Abstract algebra and number theory

Homomorphisms, quotients and the structure of groups

Abstract algebra and number theory · Lesson 2 of 4

Lesson 2 of 4

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Unit 6

Abstract algebra and number theory

4 lessons · 4 h 55 min of study

Groups, subgroups, cyclic and permutation groups1 h 15 min of study
Homomorphisms, quotients and the structure of groupsReading · 0%
Rings, ideals, fields and polynomials1 h 10 min of study
Number theory1 h 10 min of study

This unit is ≈12% of the GRE Math, across 4 lessons. Full syllabus

Lesson 2 of 4 · Abstract algebra and number theory

Homomorphisms, quotients and the structure of groups

3 quick checks≈3% of the testStretch: Stretch: harder material that separates the top grades

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By the end you’ll be able to

Identify homomorphisms, kernels and images and apply the first isomorphism theorem
Recognise normal subgroups, form quotient groups and find centres of groups
Classify finite abelian groups with the fundamental theorem and count the abelian groups of a given order

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Adaptive questions on homomorphisms, quotients and the structure of groups.

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0% read

Apply Cauchy’s theorem and elementary Sylow theorems to decide existence of subgroups and simplicity

Decide whether two groups are isomorphic using invariants (order, element orders, abelian or cyclic structure, direct products)

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