I feel like I talk group theory a lot in these A-to-Z sequences. Some of that’s deserved. Group theory underlies a lot of modern mathematics. Part of it is surely that it made the deepest impression on me, as a mathematics major, even though my work ended up not touching groups often. **Quotient Groups** are at that nice intersection of being important yet having a misleading name. You’re introduced to them after learning about groups, which have an operation that works like addition/subtraction; and then rings, which have addition/subtraction plus multiplication. Surely a quotient group is just a ring with division, right? No, it is not. But, lucky thing, there’s one quotient group you certainly know and feel familiar with. You’ll see.

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## Author: Joseph Nebus

I was born 198 years to the day after Johnny Appleseed. The differences between us do not end there. He/him.
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