Results about Size of Order of Abelian finite Groups with Perfect Order Subsets Contained Sylow-p Subgroups
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abelian groups with perfect order subsets, cyclic sylow-p subgroups, minimal groups with perfect order subsets, order of groups.
Abstract
The purpose of this paper is presenting groups with perfect order subsets (or POS groups) which have made by the mathematicians Carrie Finch and Lenny Jones in 2002, and also presenting theorems and results about order of these groups. This study showed that if G is a minimal abelian finite group with perfect order subsets where the indexes of cyclic sylow-p subgroups are prime numbers do not divide/G/ , and not isomorphic to any of the main nine groups which not have the identified indexes, then /G/ almost goes to infinity.
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