More R-sequenceable Groups
نویسنده
چکیده
منابع مشابه
R-sequenceability and R*-sequenceability of abelian 2-groups
A group of order n is said to be R-sequenceable if the nonidentity elements of the group can be listed in a sequence a,, a,, . . . , a,_ 1 such that the quotients a; ‘az, a; ’ a3, . , a;?,a,_ r, a.-_‘,a, are distinct. An abelian group is R*-sequenceable if it has an R-sequencing a,, a,, . . , a,, _ 1 such that a,_ ra, + r = ai for some i (subscripts are read modulo n 1). Friedlander, Gordon and...
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In 1980, about 20 years after sequenceable groups were introduced by Gordon to construct row-complete latin squares, Keedwell published a survey of all the available results concerning sequencings. This was updated (jointly with Dénes) in 1991 and a short overview, including results about complete mappings and Rsequencings, was given in the CRC Handbook of Combinatorial Designs in 1995. In Sect...
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We construct narcissistic terraces for cyclic groups that have various properties which enable the construction of R-sequencings and strong halfcycles for many non-cyclic abelian groups. Among other results, we show: that an abelian group which is isomorphic to a direct product of cyclic factors such that the number of factors of order congruent to 3 (mod 4) of order at most 79 is at least as l...
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The problem of finding R-sequencings for abelian groups of even orders has been reduced to that of finding R∗sequencings for abelian groups of odd orders except in the case when the Sylow 2-subgroup is a non-cyclic non-elementary-abelian group of order 8. We partially address this exception, including all instances when the group has order 8t for t congruent to 1, 2, 3 or 4 (mod 7). As much is ...
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عنوان ژورنال:
- Australasian J. Combinatorics
دوره 37 شماره
صفحات -
تاریخ انتشار 2007