The products of conjugacy classes in some infinite simple groups

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Let H ν =S/S ν, where S is the group of all permutations of a set of cardinality א ν and S v is its subgroup of permutations moving less than א ν elements. The infinite simple groups H ν, ν>0, have covering number two; that is, C 2=H ν holds for each nonunit conjugacy class C[M]. Janko's small group J 1, the only finite simple group with covering number two, satisfies also: {Mathematical expression}. In fact, H ν (ν>0) are the only groups of covering number two where (*) is known to fail. In this paper we determine arbitrary products of classes in H ν (ν>0).

Original languageEnglish
Pages (from-to)54-74
Number of pages21
JournalIsrael Journal of Mathematics
Issue number1-2
StatePublished - Mar 1985

ASJC Scopus subject areas

  • General Mathematics


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