Involution fusion pattern

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This article defines an equivalence relation over the collection of groups. View a complete list of equivalence relations on groups.
This term is related to: Classification of finite simple groups
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Definition

Definition with symbols

Two groups G and G^* are said to have the same involution fusion pattern if there is an isomorphism x \mapsto x^* from a 2-Sylow subgroup S of G to a 2-Sylow subgroup S^* of G^* such that x,y \in S are conjugate in G if and only if x^*, y^* are conjugate elements in S^*.

Relation with other equivalence relations

Stronger equivalence relations