JP Journal of Algebra, Number Theory and Applications
Volume 2, Issue 2, Pages 111 - 119
(August 2002)
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ON
THETA-COMPLETIONS AND s-COMPLETIONS FOR
MAXIMAL SUBGROUPS
Zhao Yaoqing (P. R. China)
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Abstract: For a maximal subgroup M
of a group G, an s-completion
for M is a Deskins completion C such
that either C = G or there exists a
subgroup D of G which is not a
completion for M and D contains C
as a maximal subgroup. This concept was introduced
by Li Shirong and Zhao Yaoqing and it weakens the
imposed maximalities on completions as usually did
in investigating the classification of finite
groups. In this paper, we study the solvability and
supersolvability of finite groups by means of s-completions
and q-completions. |
Keywords and phrases: q
-completion, s-completion, completion,
maximal subgroup. |
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