0000000000512593

AUTHOR

Azahara Sáez

showing 2 related works from this author

Existence of normal Hall subgroups by means of orders of products

2018

Let G be a finite group, let π be a set of primes and let p be a prime. We characterize the existence of a normal Hall π‐subgroup in G in terms of the order of products of certain elements of G. This theorem generalizes a characterization of A. Moretó and the second author by using the orders of products of elements for those groups having a normal Sylow p‐subgroup 6. As a consequence, we also give a π‐decomposability criterion for a finite group also by means of the orders of products.

010101 applied mathematicsPure mathematicsp-nilpotent groupsGeneral Mathematics010102 general mathematicsproduct of elements0101 mathematics01 natural sciencesHall subgroupsMathematicsorder of elements
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Order of products of elements in finite groups

2018

If G is a finite group, p is a prime, and x∈G, it is an interesting problem to place x in a convenient small (normal) subgroup of G, assuming some knowledge of the order of the products xy, for certain p‐elements y of G.

Order (business)General Mathematics010102 general mathematics0103 physical sciencesApplied mathematics010307 mathematical physics0101 mathematics01 natural sciencesfinite groupsMathematics
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