Abstract
Total groups are groups for which the dimension of the invariant algebra center of a central simple algebra 𝔄 f associated to a 2-cocycle f∈Z 2 (Gal(L/k),L * ) under a lifting of the Galois action to 𝔄 f is constant for all k and f. In this article, we show that the quasi-CC groups (groups with cyclic center and for which all the centralizer of non-central elements are cyclic) are total. CC-groups, which are quasi-CC groups with trivial center, are thus total. We give a complete classification of these groups. We also describe a general family of quasi-CC groups which are not CC: the meta-dicyclic groups.
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