Sandwich classification theorem
عنوان مقاله: Sandwich classification theorem
شناسه ملی مقاله: JR_THEGR-4-3_003
منتشر شده در در سال 1394
شناسه ملی مقاله: JR_THEGR-4-3_003
منتشر شده در در سال 1394
مشخصات نویسندگان مقاله:
Alexey Stepanov - St.Petersburg State University
خلاصه مقاله:
Alexey Stepanov - St.Petersburg State University
The present note arises from the author's talk at the conference ``Ischia Group Theory ۲۰۱۴''. For subgroups F\le N of a group G denote by L(F,N) the set of all subgroups of N, containing F. Let D be a subgroup of G. In this note we study the lattice LL=L(D,G) and the lattice LL' of subgroups of G, normalized by D. We say that LL satisfies sandwich classification theorem if LL splits into a disjoint union of sandwiches L(F,N_G(F)) over all subgroups F such that the normal closure of D in F coincides with F. Here N_G(F) denotes the normalizer of F in G. A similar notion of sandwich classification is introduced for the lattice LL'. If D is perfect, i.\,e. coincides with its commutator subgroup, then it turns out that sandwich classification theorem for LL and LL' are equivalent. We also show how to find basic subroup F of sandwiches for LL' and review sandwich classification theorems in algebraic groups over rings.
کلمات کلیدی: subgroup structure, sandwich classification, Chevalley groups, commutative rings
صفحه اختصاصی مقاله و دریافت فایل کامل: https://civilica.com/doc/1199969/