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We describe abstract groups using standard building blocks:

  • $C_n$ denotes the cyclic group of order $n$
  • $D_n$ denotes the dihedral group of order $2n$
  • $A_n$ denotes the alternating group on $n$ letters
  • $S_n$ denotes the symmetric group on $n$ letters

Groups $A$ and $B$ may be used to construct a larger group:

  • $A\times B$ for the direct product of $A$ and $B$
  • $A:B$ for the semidirect product of $A$ and $B$ (with normal subgroup $A$)
  • $A.B$ an extension with normal subgroup $A$ and quotient isomorphic to $B$
  • $A\wr B$ for the wreath product of A and B
Knowl status:
  • Review status: reviewed
  • Last edited by Manami Roy on 2020-11-20 15:30:18
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