A partition for the elements of prime-power order in a finite group G is a family of subgroups with the property that every non-identity element of prime-power order lies in exactly one subgroup of the family. The main result of this paper is a classification of the finite simple groups which have such a partition. We also establish a connection between this concept and the class of permutation groups all of whose elements of prime-power order have the same number of fixed points. © de Gruyter 2006
Spiga, P. (2006). Finite simple groups admitting a partition for the elements of prime-power order. JOURNAL OF GROUP THEORY, 9(2), 219-229 [10.1515/JGT.2006.015].
Finite simple groups admitting a partition for the elements of prime-power order
SPIGA, PABLO
2006
Abstract
A partition for the elements of prime-power order in a finite group G is a family of subgroups with the property that every non-identity element of prime-power order lies in exactly one subgroup of the family. The main result of this paper is a classification of the finite simple groups which have such a partition. We also establish a connection between this concept and the class of permutation groups all of whose elements of prime-power order have the same number of fixed points. © de Gruyter 2006
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