Tagged Questions

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Why are centers, centralizers and normalizers called that way?

I know what they are, but where do the names come from?
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The name of a certain type of groups

What is the name (if any) given to groups satisfying: $$\forall x,y,z\in G [xyx^{-1}=(zxz^{-1})y(zxz^{-1})^{-1}]$$ I understand this question might not be suitable here, but I really can't search ...
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How did the Symmetric group and Alternating group come to be named as such?

The Dihedral group makes sense, "Di" means two, and "hedral" means.. shape I think (I've just realised how much of what I think words mean are guesses based on experience) like a "polygon" is a 2d ...
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Why is a perfect group called a perfect group

A group is called perfect if we have $[G,G]=G$. I was wondering in what sense is this group perfect? I've never really done anything much with perfect groups so I don't really know anything about ...
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Is there a name for this object? (Like a group, but the inverse is not necessarily a member of the set)

A group is a set $G$, together with a binary operation $\cdot$ that is closed - if $f\in G$ and $g \in G$ then $f\cdot g \in G$ is associative - $(f \cdot g) \cdot h = f \cdot (g \cdot h)$ has an ...
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Terminology concerning conjugation in groups of functions.

If there is a function $a$ such that $a\circ g\circ a^{-1}=h$ then the functions $g$ and $h$ are conjugate to each other. If one wished to identify $a$, would one say "$g$ and $h$ are conjugate "by ...
Given a set $X$, the collection of all bijective endofunctions on $X$ forms a group, called the symmetric group on $X.$ Furthermore, Cayley's theorems says that every group embeds into a subgroup of ...