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Generation of alternating groups by pairs of conjugates

Abstract

Considering the conjugacy classes of the alternating group of degreen, those classes that contain a pair of generators are in the majority. In fact, the proportion of such classes is 1 −ε(n), andε(n) → 0 asn → ∞.

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Beasley, L.B., Brenner, J.L., Erdős, P. et al. Generation of alternating groups by pairs of conjugates. Period Math Hung 18, 259–269 (1987). https://doi.org/10.1007/BF01848100

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AMS (MOS) subject classifications (1980)

  • Primary 20P05
  • Secondary 20F05, 20D06, 20D60

Key words and phrases

  • Alternating groups
  • pairs of generators in almost all conjugacy classes