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13.
Permutation groups containing a regular abelian Hall subgroup
Dobson, Edward Tauscher, 1965- ; Li, Cai Heng ; Spiga, Pablo
The authors prove some properties of the normal closure of a regular Abelian Hall ▫$\pi$▫-subgroup (assuming there is one) of a transitive permutation group. They prove the closure is permutation ...isomorphic to a direct product of cyclic groups and 2-transitive nonabelian simple groups, and give some restrictions on the number of factors and the possible nonabelian factors. What the authors did not do is define a Hall ▫$\pi$▫-subgroup: a Hall ▫$\pi$▫-subgroup is a subgroup whose order is a product of primes in ▫$\pi$▫, and whose index is not divisible by any primes in ▫$\pi$▫. In case where ▫$\pi=\{p\}$▫, this result generalises a result by Dobson on the overgroups of regular Abelian ▫$p$▫-groups.
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