# Every element is automorphic to its inverse is characteristic subgroup-closed

From Groupprops

This article gives the statement, and possibly proof, of a group property (i.e., group in which every element is automorphic to its inverse) satisfying a group metaproperty (i.e., characteristic subgroup-closed group property)

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## Statement

Suppose is a Group in which every element is automorphic to its inverse (?). Suppose is a characteristic subgroup of . Then, is also a group in which every element is automorphic to its inverse.

## Related facts

- Normal subgroup of ambivalent group implies every element is automorphic to its inverse
- Alternating group implies every element is automorphic to its inverse
- General linear group implies every element is automorphic to its inverse
- Projective general linear group implies every element is automorphic to its inverse
- Special linear group implies every element is automorphic to its inverse
- Projective special linear group implies every element is automorphic to its inverse