The normal covering number γ(G) of a finite, non-cyclic group G is the minimum number of proper subgroups such that each element of G lies in some conjugate of one of these subgroups. We find lower bounds linear in n for γ(Sn) , when n is even, and for γ(An) , when n is odd.
Bubboloni, D., Praeger, C., Spiga, P. (2020). Linear bounds for the normal covering number of the symmetric and alternating groups. MONATSHEFTE FÜR MATHEMATIK, 191(2), 229-247 [10.1007/s00605-019-01287-5].
Linear bounds for the normal covering number of the symmetric and alternating groups
Spiga P.
2020
Abstract
The normal covering number γ(G) of a finite, non-cyclic group G is the minimum number of proper subgroups such that each element of G lies in some conjugate of one of these subgroups. We find lower bounds linear in n for γ(Sn) , when n is even, and for γ(An) , when n is odd.
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