On the embedding of minimal non-M-groups. II

✍ Scribed by Robert W.van der Waall

• Publisher: Elsevier Science
• Year: 1976
• Weight: 373 KB
• Volume: 79
• Category: Article
• ISSN: 1385-7258
• DOI: 10.1016/1385-7258(76)90064-0

✦ Synopsis

All groups in this paper will be finite. Notations, definitions and conventions are as in [3] and [7]. Dt is the dihedral group of order 2t.

In [7] we proved the following THEOREM. Let G be a monomial Izon-hypersolvable growp and let N be a normal subgroup of G whose factor group G/N is cyclic of prime order. Suppose that all proper sections of N are monomial.

Then N is monomial if one of the following properties holda:

1. [G/NI#2.

2. Z(N) 'i8 not cydic or Z(N) = 1.

3. Z(G) ia not cyclic or Z(G) = 1. 4. G/02(G) is not iawphic to the abelian group of type (28, 2), a> 1, and also not isomorphic to a dihedral 2-group.