Double coset-ordering subgroup

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This article defines a subgroup property: a property that can be evaluated to true/false given a group and a subgroup thereof, invariant under subgroup equivalence. View a complete list of subgroup properties[SHOW MORE]


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Definition

Definition with symbols

A subgroup H of a group G is termed double coset-ordering if given any two double cosets HxH and HyH one cannot find g,h,g',h' such that gHxHg' \subset HyH and hHyHh' \subset HxH. In other words, the relation:

HxH \le HyH \iff \exists g,g' \qquad gHxHg' \subset HyH

is a partial order.

Relation with other properties

Stronger properties

Weaker properties