On Minimal Length Factorizations of Finite Groups
نویسندگان
چکیده
منابع مشابه
Factoring Euclidean isometries
Every isometry of a finite dimensional euclidean space is a product of reflections and the minimum length of a reflection factorization defines a metric on its full isometry group. In this article we identify the structure of intervals in this metric space by constructing, for each isometry, an explicit combinatorial model encoding all of its minimal length reflection factorizations. The model ...
متن کاملCoding Partitions of Regular Sets
A coding partition of a set of words partitions this set into classes such that whenever a sequence, of minimal length, has two distinct factorizations, the words of these factorizations belong to the same class. The canonical coding partition is the finest coding partition that partitions the set of words in at most one unambiguous class and other classes that localize the ambiguities in the f...
متن کاملSome conjectures on codes
Variable-length codes are the bases of the free submonoids of a free monoid. There are some important longstanding open questions about the structure of finite maximal codes. In this paper we discuss this conjectures and their relations with factorizations of cyclic groups.
متن کاملThe influence of S-embedded subgroups on the structure of finite groups
Let H be a subgroup of a group G. H is said to be S-embedded in G if G has a normal T such that HT is an S-permutable subgroup of G and H ∩ T ≤ H sG, where H denotes the subgroup generated by all those subgroups of H which are S-permutable in G. In this paper, we investigate the influence of minimal S-embedded subgroups on the structure of finite groups. We determine the structure the finite grou...
متن کاملOn inequivalent factorizations of a cycle
We introduce a bijection between inequivalent minimal factorizations of the n-cycle (1 2 . . . n) into a product of smaller cycles of given length and trees of a certain structure. A factorization has the type α = (α2, α3, · · · ) if it has αj factors of length j. Inequivalent factorizations are defined up to reordering of commuting factors. A factorization is minimal if no factorizations of a ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Experimental Mathematics
دوره 12 شماره
صفحات -
تاریخ انتشار 2003