# Differences

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groups [2010/07/29 18:30]
127.0.0.1 external edit
groups [2012/06/15 23:11] (current)
jipsen
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It follows that $e$ is a right-identity and that $^{-1}$gives a right It follows that $e$ is a right-identity and that $^{-1}$gives a right
inverse: $xe=x$, $xx^{-1}=e$. inverse: $xe=x$, $xx^{-1}=e$.
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-This definition shows that groups form a variety.
==Morphisms== ==Morphisms==
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permutations of a sets $X$, with composition, inverse, and identity map. permutations of a sets $X$, with composition, inverse, and identity map.
-Example 1: The general linear group $\langle GL_{n}(V),\cdot+Example 2: The general linear group$\langle GL_{n}(V),\cdot
,^{-1},I_{n}\rangle $, the collection of invertible$n\times n$,^{-1},I_{n}\rangle$, the collection of invertible $n\times n$
matrices over a vector space $V$, with matrix multiplication, inverse, and matrices over a vector space $V$, with matrix multiplication, inverse, and
identity matrix. identity matrix.
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-Example 1: [[Groups (mace)]]
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====Basic results==== ====Basic results====
-[[Groups (otter)]]
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f(18)= &5\\ f(18)= &5\\
\end{array}$\end{array}$
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Information about small groups up to size 2000: http://www.tu-bs.de/~hubesche/small.html Information about small groups up to size 2000: http://www.tu-bs.de/~hubesche/small.html