Finite group in which half or more of the elements are involutions
This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism
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A finite group in which half or more of the elements are involutions is a finite group in which the number of involutions (i.e., elements of order equal to ) is half or more of the order of the group.
This property is determined completely by looking at the order statistics of the group.
Groups of order powers of
|List of groups of order in which half or more of the elements are involutions||List of GAP IDs (in same order)||Those groups in this list that are not generalized dihedral groups||List of GAP IDs (in same order)|
|3||8||dihedral group:D8, elementary abelian group:E8||3, 5||--|
|4||16||dihedral group:D16, direct product of D8 and Z2, elementary abelian group:E16||7, 11, 14||--|
|5||32||dihedral group:D32, SmallGroup(32,27), generalized dihedral group for direct product of Z4 and Z4, direct product of D16 and Z2, direct product of D8 and V4, inner holomorph of D8, elementary abelian group:E32||18, 27, 34, 39, 45, 49, 51||SmallGroup(32,27), inner holomorph of D8||27, 49|
|6||64||(too long to list)||52, 174, 186, 202, 211, 226, 250, 261, 264, 267||direct product of SmallGroup(32,27) and Z2, direct product of D8 and D8, direct product of SmallGroup(32,49) and Z2||202, 226, 264|
Groups of other orders
For all other orders, the only examples are the generalized dihedral groups.