Some sufficient conditions for a nilpotent group. (English) Zbl 0778.20011
Several sufficient conditions are posed in order that a finite group be nilpotent. In most of them the notion of “semi-normal” plays a rôle. Here, a subgroup \(A\) of a group \(G\) is said to be semi-normal in \(G\) if there exists \(B\leq G\) with \(AB=G\) but with \(AC<G\) for every \(C<B\).
Reviewer’s remarks: 1. The use of the English language is mediocre. 2. The name of the reviewer is mispelled in the paper, whenever possible, in distinct ways. 3. There are some (obvious) misprints in the mathematics. 4. The example as constructed on page 292, is precisely the same example as mentioned in the Introduction of the reviewer’s paper [in J. Reine Angew. Math. 285, 77-78 (1976; Zbl 0326.20020)], despite the comment by the author on page 293.
Reviewer’s remarks: 1. The use of the English language is mediocre. 2. The name of the reviewer is mispelled in the paper, whenever possible, in distinct ways. 3. There are some (obvious) misprints in the mathematics. 4. The example as constructed on page 292, is precisely the same example as mentioned in the Introduction of the reviewer’s paper [in J. Reine Angew. Math. 285, 77-78 (1976; Zbl 0326.20020)], despite the comment by the author on page 293.
Reviewer: R.W.van der Waall (Amsterdam)
MSC:
| 20D15 | Finite nilpotent groups, \(p\)-groups |
| 20D35 | Subnormal subgroups of abstract finite groups |
| 20D40 | Products of subgroups of abstract finite groups |
Citations:
Zbl 0326.20020References:
| [1] | Su, X., Semi-normal subgroups of a finite group, Math. Mag., 8, 7-9 (1988) · Zbl 0687.20024 |
| [2] | Robinson, J. S., A Course in the Theory of Groups (1980), Springer-Verlag: Springer-Verlag New York/Heidelberg/Berlin · Zbl 0453.20001 |
| [3] | Huppert, B., Endliche Gruppen (1967), Springer-Verlag: Springer-Verlag Berlin · Zbl 0217.07201 |
| [4] | Buckley, J., Finite groups whose minimal subgroups are normal, Math. Z., 116, 15-17 (1970) · Zbl 0202.02303 |
| [5] | van der Waal, R., On minimal subgroups which are normal, J. Reine Angew. Math., 285, 77-78 (1976) · Zbl 0326.20020 |
| [6] | Zhang, Y., (Structure of Finite Group, Vol. 2 (1982), Science: Science Beijing), 714 |
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