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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
Posted in Notes
Tagged abelian groups, advanced, direct products, direct sums, free groups, generated groups, universal properties
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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
Posted in Notes
Tagged advanced, free groups, generated groups, group theory, universal property
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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
Posted in Notes
Tagged cyclic groups, generated groups, group theory applications, groups, intermediate, number theory, subgroups
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Mathematics and Such 