No the global jira-administrators only have the right to control the security, notification, issue types, workflow schema etc.
For the project-administrators: This includes the ability to edit project role membership, project components, project versions and some project details ('Project Name', 'URL', 'Project Lead', 'Project Description')."
For more details see https://confluence.atlassian.com/display/AOD/Managing+Project+Permissions
Hope this helps you, Thanks.
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