Roland Schmidt
Supermodulare Untergruppen von Gruppen
The paper is published: Rostocker Mathematisches Kolloquium, Rostock. Math. Kolloq. 53, 23-49 (1999)

MSC:

20E15 Chains and lattices of subgroups, subnormal subgroups, See also {20F22}

20D30 Series and lattices of subgroups

Abstract: Nach [9] heisst das Element $M$ des Verbandes ${\cal V}$
{\it supermodular} in ${\cal V}$ (kurz $M$ sm ${\cal V}$), wenn
fuer alle $B,C,D\in {\cal V}$ die folgende Identitaet erfuellt
ist:
\[ (M\cu B)\cp (M\cu C)\cp (M\cu D)=
M \cu (B\cp C\cp (M\cu D))\cu (C\cp D\cp (M\cu B))\cu(B\cp D\cp
(M\cu C));
\]
$M$ heisst {\it vereinigungsdistributiv} (kurz: $\cup$-distributiv) in ${\cal V}$, wenn
fuer alle $B,C\in {\cal V}$ das distributive Gesetz
\[ M \cu (B\cp C)=(M\cu B)\cp (M\cu C)$}\hfill(D)
\] gilt.
Keywords: Chains and lattices of subgroups, subnormal subgroups, Other classes of groups defined by subgroup chains, Series and lattices of subgroups