We prove that any finite nonsolvable group is a product of at most 36 conjugates of a proper subgroup and we give an upper bound in the case of solvable groups.
For every non-nilpotent finite group G, there exists at least one proper subgroup M such that G is the setwise product of a finite number of conjugates of M. We define γcp(G) to be the smallest number k such that G is a product, in some order, of k pairwise conjugated proper subgroups of G. We prove that if G is non-solvable then γcp(G)≤36 while if G is solvable then γcp(G) can attain any integer value bigger than 2, while, on the other hand, γcp(G)≤4log2|G|.
Factorizing a finite group into conjugates of a subgroup
Garonzi M
;
2014
Abstract
For every non-nilpotent finite group G, there exists at least one proper subgroup M such that G is the setwise product of a finite number of conjugates of M. We define γcp(G) to be the smallest number k such that G is a product, in some order, of k pairwise conjugated proper subgroups of G. We prove that if G is non-solvable then γcp(G)≤36 while if G is solvable then γcp(G) can attain any integer value bigger than 2, while, on the other hand, γcp(G)≤4log2|G|.File in questo prodotto:
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