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group theory, a quasinormal subgroup, or permutable subgroup, is a subgroup of a group that commutes (permutes) with every other subgroup with respect to
Quasinormal_subgroup
Subgroup invariant under conjugation
Descendant subgroup Quasinormal subgroup Seminormal subgroup Conjugate permutable subgroup Modular subgroup Pronormal subgroup Paranormal subgroup Polynormal
Normal_subgroup
proof that for finite groups, every quasinormal subgroup is a subnormal subgroup. Clearly, every quasinormal subgroup is conjugate-permutable. In fact,
Conjugate-permutable_subgroup
and abnormal subgroups". J. Math. Study. 29 (4): 10–15. Zhang, Q. H. (1998). "Finite groups with only ss-quasinormal and abnormal subgroups". Northeast
Abnormal_subgroup
Every quasinormal subgroup, and, more generally, every conjugate-permutable subgroup, of a finite group is subnormal. Every pronormal subgroup that is
Subnormal_subgroup
defined by the subgroup generated by the union of subgroups. By the modular property of groups, every quasinormal subgroup (that is, a subgroup that permutes
Modular_subgroup
definition of seminormal subgroups is due to Xiang Ying Su. Every normal subgroup is seminormal. For finite groups, every quasinormal subgroup is seminormal. Su
Seminormal_subgroup
Lattice whose elements are the subgroups of a given group
lattice is modular is that subgroups commute with each other, i.e. that they are quasinormal subgroups. Nilpotent normal subgroups form a lattice, which is
Lattice_of_subgroups
Representation of the symmetry group of spacetime in special relativity
Chapter 8 pp. 307–310. Gonzalez, P. A.; Vasquez, Y. (2014), "Dirac Quasinormal Modes of New Type Black Holes in New Massive Gravity", Eur. Phys. J.
Representation theory of the Lorentz group
Representation_theory_of_the_Lorentz_group
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