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Finite equilibrated groups. (English) Zbl 0891.20015
The titular $$E$$-groups are finite groups $$G$$ in which no subgroup $$G_1$$ can be expressed as the product of non-normal subgroups of $$G_1$$. The authors determine the simple nonabelian $$E$$-groups: the $$L_2(p)$$ where $$p$$ is a prime, $$p\equiv 5 \bmod 8$$, $$p^2\equiv-1\bmod 5$$, $$p+1$$ is twice a prime power and $$p-1$$ is four times a prime power. And solvable $$E$$-groups $$C$$ have many nice properties: $$G$$ is an extension of a $$p$$-group by a Dedekind group and the order of $$G'$$ is either a prime power or twice a prime power. In Section 4 $$E$$-groups of prime power order are investigated and it is shown that for $$p>3$$ all except one are of class at most 2. It is noted that the situation looks more complicated for $$p=2$$.

##### MSC:
 20D40 Products of subgroups of abstract finite groups 20D10 Finite solvable groups, theory of formations, Schunck classes, Fitting classes, $$\pi$$-length, ranks 20D15 Finite nilpotent groups, $$p$$-groups 20D05 Finite simple groups and their classification
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##### References:
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