Тип публикации: статья из журнала
Год издания: 2006
Идентификатор DOI: 10.1007/s11202-006-0077-7
Ключевые слова: factorization; weakly complemented subgroup; finite simple group; maximal subgroup
Аннотация: We study Problem 8.31 in [1] of the description of finite weakly factorizable groups, i.e., the groups whose every proper subgroup is complemented in a larger subgroup. By Lemma 1 of [2], the subdirect product of a completely factorizable group (such groups were studied by Ph. Hall and N.V. Baeva (Chernikova)) and a weakly factorizable group is a weakly factorizable group. In connection with a remark in [2], we observe that a dihedral 2-group is always weakly factorizable but, in general, it cannot even be obtained from the groups of prime order by repeated application of the lemma. Theorem 1, basing on the available maximal factorizations, shows that there exist exactly three finite simple nonabelian groups with complemented maximal subgroups. Theorem 2 confirms the conjecture of [2] on uniqueness of a finite simple nonabelian group with the property of weak factorizability. Earlier Theorems 1 and 2 were proven in special cases by A.G. Likharev.
Издание
Журнал: SIBERIAN MATHEMATICAL JOURNAL
Выпуск журнала: Vol. 47, Is. 4
Номера страниц: 659-668
ISSN журнала: 00374466
Место издания: NEW YORK
Издатель: CONSULTANTS BUREAU/SPRINGER
Персоны
- Levchuk V.M. (Krasnoyarsk State University)
- Likharev A.G. (Krasnoyarsk State University)
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