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Keywords:
loop; dihedral group; inner mapping group
loop; dihedral group; inner mapping group
Summary:
We show that finite commutative inverse property loops may not have nonabelian dihedral 2-groups as their inner mapping group.
References:
[1] Bruck R. H.: Contributions to the theory of loops. Trans. Amer. Math. Soc. 60 (1946), 245–354. DOI 10.1090/S0002-9947-1946-0017288-3 | MR 0017288 | Zbl 0061.02201
[2] Drápal A.: A class of commutative loops with metacyclic inner mapping groups. Comment. Math. Univ. Carolin. 49 (2008), no. 3, 357–382. MR 2490433
[3] Niemenmaa M.: Finite loops with nilpotent inner mapping groups are centrally nilpotent. Bull. Aust. Math. Soc. 79 (2009), no. 1, 109–114. DOI 10.1017/S0004972708001093 | MR 2486887 | Zbl 1167.20039
[4] Niemenmaa M.: On finite commutative IP-loops with elementary abelian inner mapping groups of order $p^4$. Comment. Math. Univ. Carolin. 51 (2010), no. 4, 559–563. MR 2858260
[5] Niemenmaa M., Kepka T.: On multiplication groups of loops. J. Algebra 135 (1990), no. 1, 112–122. DOI 10.1016/0021-8693(90)90152-E | MR 1076080 | Zbl 0706.20046
[6] Niemenmaa M., Kepka T.: On connected transversals to abelian subgroups. Bull. Austral. Math. Soc. 49 (1994), no. 1, 121–128. DOI 10.1017/S0004972700016166 | MR 1262682 | Zbl 0799.20020
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