# Involution fusion pattern

From Groupprops

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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This article is about a definition in group theory that is standard among the group theory community (or sub-community that dabbles in such things) but is not very basic or common for people outside.VIEW: Definitions built on this | Facts about this: (factscloselyrelated to Involution fusion pattern, all facts related to Involution fusion pattern) |Survey articles about this | Survey articles about definitions built on this

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## Definition

### Definition with symbols

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