# Subgroup having a twisted subgroup as transversal

This article defines a subgroup property: a property that can be evaluated to true/false given a group and a subgroup thereof, invariant under subgroup equivalence. View a complete list of subgroup properties[SHOW MORE]

## Definition

Suppose $H$ is a subgroup of a group $G$. We say that $H$ is a subgroup having a twisted subgroup as transversal if there exists a twisted subgroup $S$ of $G$ that is also a left transversal for $H$ in $G$, i.e., it intersects every left coset of $H$ in $G$ at exactly one point. Note that $S$ will automatically also be a right transversal for $H$ in $G$.

## Relation with other properties

### Stronger properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
direct factor (via permutably complemented) (via permutably complemented) |FULL LIST, MORE INFO

### Weaker properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions