Involution fusion pattern

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

• Centralizer of involution pattern