Involution fusion pattern

From Groupprops
Jump to: navigation, search
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
View other terms related to Classification of finite simple groups | View facts related to Classification of finite simple groups

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: (facts closely related to Involution fusion pattern, all facts related to Involution fusion pattern) |Survey articles about this | Survey articles about definitions built on this
VIEW RELATED: Analogues of this | Variations of this | Opposites of this |
View a list of other standard non-basic definitions


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