Sentence examples for mutually permutable subgroups from inspiring English sources

Then, G is the product of the mutually permutable subgroups H and K. Proof.

We determine that G is the mutually permutable product of the subgroups H and K.

Following Carocca [4], we say that the subgroups H and K of a group G are mutually permutable if H commutes with every subgroup of K and K commutes with every subgroup of H.

We say that H and K are mutually permutable if H commutes with every subgroup of K and K commutes with every subgroup of H. Definition 2.2.[5].

If G=HK and H and K are mutually permutable, we say that G is the mutually permutable product of the subgroups H and K.

It is an interesting topic in group theory to study the generalized permutable subgroups and generalized supplemented subgroups.

In [2], Skiba introduced the concepts of weakly S-permutable subgroups and weakly S-supplemented subgroups.

Since many relevant families of subgroups, such as normal subgroups, (S- quasinormal S- quasinormal(subgroupsable subgrorpS- permutableS- permutablemplemented subgroups, c-normalmented subgroups, weakly S-supplemented subgroups and S-quasinormally embedded subgroups, enjoy the λ-supplementary property, a lot of nicomplementedollow from Theorem 3.2.

Table 2 Comparison of methods across five different datasets using fivefold cross validation Method GMean F1Score F0.5Score RandomOrder-10 51.14 36.84 46.44 DRABAL 61.05a 51.11a 64.51.14he HTS assays data is partitioned into five approximately equally sized mutually distinct subgroups such that a single subgroup representing 20% of the data is retained for testing only.

Using a typical fivefold cross-validation, the HTS assays data is partitioned into five approximately equally sized mutually distinct subgroups such that a single subgroup representing 20% of the data is retained for testing only and is not used in any way for developing the model.

Theoretically, opposite effects in mutually exclusive subgroups could also be responsible.