Definition of Subgroups. Meaning of Subgroups. Synonyms of Subgroups

- have infinite order. The subgroups of any given group form a complete lattice under inclusion, called the lattice of subgroups. (While the infimum here...
- congruence subgroup problem, which asks whether all subgroups of finite index are essentially congruence subgroups. Congruence subgroups of 2 × 2 matrices...
- given generalized ****ing subgroup. The normalizers of nontrivial p-subgroups of a finite group are called the p-local subgroups and exert a great deal of...
- algebraic groups. Subgroups between a Borel subgroup B and the ambient group G are called parabolic subgroups. Parabolic subgroups P are also characterized...
- of G, but G has no subgroups of these orders. The simple group of order 168 has two different conjugacy classes of Hall subgroups of order 24 (though...
- Subgroup analysis refers to repeating the analysis of a study within subgroups of subjects defined by a subgrouping variable. For example: smoking status...
- that any finite solvable group has a Carter subgroup, and all its Carter subgroups are conjugate subgroups (and therefore isomorphic). If a group is not...
- group then its unique maximal subgroup (as a semigroup) is S itself. Considering subgroups, and in particular maximal subgroups, of semigroups often allows...
- subgroups are important because they (and only they) can be used to construct quotient groups of the given group. Furthermore, the normal subgroups of...
- not a proper subgroup of any other p {\displaystyle p} -subgroup of G {\displaystyle G} . The set of all Sylow p {\displaystyle p} -subgroups for a given...