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Keywords:
2-groups; distances of groups
2-groups; distances of groups
Summary:
The paper reports the results of a search for pairs of groups of order $n$ that can be placed in the distance $n^2/4$ for the case when $n\in \{16,32\}$. The constructions that are used are of the general character and some of their properties are discussed as well.
References:
[1] Donovan D., Oates-Williams S., Praeger Ch.E.: On the distance between distinct group Latin squares. J. Combin. Des. 5 (1997), 235-248. MR 1451283 | Zbl 0912.05021
[2] Drápal A.: How far apart can the group multiplication table be?. European J. Combin. 13 (1992), 335-343. MR 1181074
[3] Drápal A.: Non-isomorphic $2$-groups coincide at most in three quarters of their multiplication tables. European J. Combin. 20 (2000), 301-321. MR 1750166
[4] Vojtěchovský P.: O Hammingově vzdálenosti grup. M.D. Thesis (in Czech), Charles University, Prague, 1998.
[5] Zhukavets N.: Close $2$-groups. Ph.D. Thesis, Charles University, Prague, in preparation.
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