Groups with small deviation for non-subnormal subgroups

• Autorzy: Leonid Kurdachenko , Howard Smith
• Języki publikacji: EN

Abstrakty

EN

We introduce the notion of the non-subnormal deviation of a group G. If the deviation is 0 then G satisfies the minimal condition for nonsubnormal subgroups, while if the deviation is at most 1 then G satisfies the so-called weak minimal condition for such subgroups (though the converse does not hold). Here we present some results on groups G that are either soluble or locally nilpotent and that have deviation at most 1. For example, a torsion-free locally nilpotent with deviation at most 1 is nilpotent, while a Baer group with deviation at most 1 has all of its subgroups subnormal.

Słowa kluczowe

EN

Non-subnormal subgroups; Small deviation

Kategorie tematyczne

• 20E15: Chains and lattices of subgroups, subnormal subgroups
• 20F16: Solvable groups, supersolvable groups
• 20F19: Generalizations of solvable and nilpotent groups

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2009
• Tom: 7
• Numer: 2
• Strony: 186-199

Daty

wydano

2009-06-01

online

2009-05-24

Twórcy

autor

Leonid Kurdachenko

• Algebra Department, Dnepropetrovsk University, Dnepropetrovsk, Ukraine

autor

Howard Smith

• Department of Mathematics, Bucknell University, Lewisburg, USA

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-009-0012-9