Geodesic
The classification of finite groups by using iteration digraphs
Czechoslovak Mathematical Journal, Tome 66 (2016) no. 4, pp. 1103-1117.

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A digraph is associated with a finite group by utilizing the power map f:G→G defined by f(x)=xk for all x∈G, where k is a fixed natural number. It is denoted by γG(n,k). In this paper, the generalized quaternion and 2-groups are studied. The height structure is discussed for the generalized quaternion. The necessary and sufficient conditions on a power digraph of a 2-group are determined for a 2-group to be a generalized quaternion group. Further, the classification of two generated 2-groups as abelian or non-abelian in terms of semi-regularity of the power digraphs is completed.
DOI : 10.1007/s10587-016-0312-8
Classification : 05C20, 05C25, 05C50, 20B25, 20D15
Mots-clés : 2-group; generalized quaternion group; iteration digraph; cycle; indegree; fixed point; regular digraph 
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     title = {The classification of finite groups by using iteration digraphs},
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Ahmad, Uzma; Moeen, Muqadas. The classification of finite groups by using iteration digraphs. Czechoslovak Mathematical Journal, Tome 66 (2016) no. 4, pp. 1103-1117. doi : 10.1007/s10587-016-0312-8. https://geodesic-test.mathdoc.fr/articles/10.1007/s10587-016-0312-8/

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