### 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(S
_{n}
) , when n is even, and for γ(A
_{n}
) , when n is odd.

Original language | English |
---|---|

Number of pages | 19 |

Journal | Monatshefte fur Mathematik |

DOIs | |

Publication status | E-pub ahead of print - 20 Mar 2019 |

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**Linear bounds for the normal covering number of the symmetric and alternating groups.** / Bubboloni, Daniela; Praeger, Cheryl E.; Spiga, Pablo.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Linear bounds for the normal covering number of the symmetric and alternating groups

AU - Bubboloni, Daniela

AU - Praeger, Cheryl E.

AU - Spiga, Pablo

PY - 2019/3/20

Y1 - 2019/3/20

N2 - 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(S n ) , when n is even, and for γ(A n ) , when n is odd.

AB - 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(S n ) , when n is even, and for γ(A n ) , when n is odd.

KW - Conjugacy classes

KW - Normal coverings

KW - Partitions

KW - Symmetric groups

UR - http://www.scopus.com/inward/record.url?scp=85063228864&partnerID=8YFLogxK

U2 - 10.1007/s00605-019-01287-5

DO - 10.1007/s00605-019-01287-5

M3 - Article

JO - MONATSHEFTE FÜR MATHEMATIK

JF - MONATSHEFTE FÜR MATHEMATIK

SN - 0026-9255

ER -