Complemented group

In mathematics, in the realm of group theory, the term complemented group is used in two distinct, but similar ways.

The following are equivalent for any finite group G: Later, in (Zacher 1953), a group is said to be complemented if the lattice of subgroups is a complemented lattice, that is, if for every subgroup H there is a subgroup K such that H ∩ K = 1 and ⟨H, K ⟩ is the whole group.

Such groups are also called K-groups in the Italian and lattice theoretic literature, such as (Schmidt 1994, pp.

Note that in the classification of finite simple groups, K-group is more used to mean a group whose proper subgroups only have composition factors amongst the known finite simple groups.

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