Left-transitively WNSCDIN not implies normal
This article gives the statement and possibly, proof, of a non-implication relation between two subgroup properties. That is, it states that every subgroup satisfying the first subgroup property (i.e., left-transitively WNSCDIN-subgroup) need not satisfy the second subgroup property (i.e., normal subgroup)
View a complete list of subgroup property non-implications | View a complete list of subgroup property implications
Get more facts about left-transitively WNSCDIN-subgroup|Get more facts about normal subgroup
EXPLORE EXAMPLES YOURSELF: View examples of subgroups satisfying property left-transitively WNSCDIN-subgroup but not normal subgroup|View examples of subgroups satisfying property left-transitively WNSCDIN-subgroup and normal subgroup
Example of a subgroup of order two
Further information: dihedral group:D8
Let be any group with a non-normal subgroup of order two. Then, is left-transitively WNSCDIN in .
For a concrete example, take to be a dihedral group and to be a subgroup of order two generated by a reflection element.