Recently, increasing attention has been focused on the investigation of the human brain connectome that describes the patterns of structural and functional connectivity networks of the human brain.Since Z(G) is a nontrivial subgroup, Z(G) must divide the order of the group, so the. To classify the groups of order 16, we consider the di erent cases for the order of the center. Theorem 1.2 The center of a group is also a normal subgroup (Judson, 186). Theorem 1.1 For a p-group, The center of a group is a nontrivial subgroup (Judson, 186).permutations, matrices) then we say we have a faithful.
In general, if an abstract group \(G\) is isomorphic to some concrete mathematical group (e.g. The permutation group \(G'\) associated with a group \(G\) is called the regular representation of \(G\). The set of these permutations forms a subgroup \(G'\) of \(S_n\), and \(G' \cong G\).
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