Glasnik Matematicki, Vol. 43, No.2 (2008), 321-335.

FINITE NONNILPOTENT GROUPS WITH FEW HEIGHTS OF NONNORMAL SUBGROUPS

Yakov Berkovich

Department of Mathematics, University of Haifa, Mount Carmel, Haifa 31905, Israel
e-mail: berkov@math.haifa.ac.il

Abstract.   The number of prime factors of the order of a group G (multiplicities counted) is said to be the height of G and denoted by nλ(G). We classify the nonnilpotent groups G with nλ(G) = 2 and nonsolvable groups G with nλ(G) in {3,4}.

2000 Mathematics Subject Classification.   20D25.

Key words and phrases.   Height, solvable group, Carter subgroup.

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DOI: 10.3336/gm.43.2.07

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