Abstract
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 language | English |
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Pages (from-to) | 54-74 |
Number of pages | 21 |
Journal | Israel Journal of Mathematics |
Volume | 50 |
Issue number | 1-2 |
DOIs | |
State | Published - Mar 1985 |
ASJC Scopus subject areas
- General Mathematics