We establish necessary conditions under which is contained in a unique
maximal subgroup H for a cyclic Sylow p-subgroup P of a quasisimple group G.
We then use these results to establish necessary and in most cases sufficient conditions
for the special case in which H is a p-local subgroup.
Groups satisfying these hypotheses (including the p-local hypothesis) are precisely the groups
possessing unfaithful minimal Heilbronn characters, and are relevant to the study
of Artin's conjecture on the holomorphy of L-series. Moreover, since in this case is necessarily
strongly p-embedded in G, this work complements existing results pertaining to strongly
p-embedded subgroups of groups with noncyclic Sylow p-subgroups.
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The Journal of Group Theory is devoted to the publication of original research articles in all aspects of group theory. Articles concerning applications of group theory and articles from research areas which have a significant impact on group theory will also be considered.