On the rarity of quasinormal subgroups
Let G be a non-periodic locally solvable group. A characterization is given of the subgroups-D of G for which the map , for all , defines a lattice-endomorphism.
Let be any group and let be an abelian quasinormal subgroup of . If is any positive integer, either odd or divisible by , then we prove that the subgroup is also quasinormal in .
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