Classification of cyclic braces, II

Rump, Wolfgang

doi:10.1090/tran/7569

Classification of cyclic braces, II
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Trans. Amer. Math. Soc. 372 (2019), 305-328 Request permission

Abstract:

Groups $G$ with a bijective 1-cocycle onto a right $G$-module $A$ are said to be braces. If the additive group $A$ is finite, the adjoint group $G$ of the brace is solvable. Most of the known solvable groups can be made into braces. Etingof et al. [Duke Math. J. 100 (1999), pp. 169–209] raised the question to classify T-structures, which are equivalent to cyclic braces. This problem is solved in the paper. The adjoint groups of finite cyclic braces are characterized as solvable, 2-nilpotent, and almost Sylow-cyclic groups. For these groups, the possible brace structures are classified.

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