Tag Archives: generated groups

Intermediate Group Theory (6)

In this post, we’ll only focus on additive abelian groups. By additive, we mean the underlying group operation is denoted by +. The identity and inverse of x are denoted by 0 and –x respectively. Similarly, 2x+3y refers to x+x+y+y+y. Etc … Continue reading

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Intermediate Group Theory (5)

Free Groups To motivate the concept of free groups, let’s consider some typical group G and elements a, b of G. Recall that , the subgroup generated by {a, b}, is defined to be the intersection of all subgroups of G containing a and b. Immediately, we see … Continue reading

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Casual Introduction to Group Theory (3)

Subgroups [ This article approximately corresponds to chapter III of the group theory blog. ] Let G be a group under operation *. If H is a subset of G, we wish to turn H into a group by inheriting the operation from G. Clearly, … Continue reading

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