diff --git a/lisp/progmodes/flymake.el b/lisp/progmodes/flymake.el
index 8a072b94a17..e911faf603d 100644
--- a/lisp/progmodes/flymake.el
+++ b/lisp/progmodes/flymake.el
@@ -1891,6 +1891,10 @@ TYPE is usually keyword `:error', `:warning' or `:note'."
   (let ((map (make-sparse-keymap)))
     (define-key map (kbd "RET") 'flymake-goto-diagnostic)
     (define-key map (kbd "SPC") 'flymake-show-diagnostic)
+    (keymap-set map "C-o" #'flymake-show-diagnostic)
+    (keymap-set map "C-m" #'flymake-goto-diagnostic)
+    (keymap-set map "n" #'next-error-this-buffer-no-select)
+    (keymap-set map "p" #'previous-error-this-buffer-no-select)
     map))
 
 (defun flymake-show-diagnostic (pos &optional other-window)
@@ -2187,6 +2191,11 @@ some of this variable's contents the diagnostic listings.")
 
 (defvar-local flymake--project-diagnostic-list-project nil)
 
+(defvar flymake-project-diagnostics-mode-map
+  (let ((map (make-sparse-keymap)))
+    (set-keymap-parent map flymake-diagnostics-buffer-mode-map)
+    map))
+
 (define-derived-mode flymake-project-diagnostics-mode tabulated-list-mode
   "Flymake diagnostics"
   "A mode for listing Flymake diagnostics in a project."
diff --git a/lisp/simple.el b/lisp/simple.el
index f686907ad68..fa173b26289 100644
--- a/lisp/simple.el
+++ b/lisp/simple.el
@@ -478,6 +478,16 @@ select the source buffer."
            '(nil (inhibit-same-window . t))))
       (next-error n))))
 
+(defun next-error-this-buffer-no-select (&optional n)
+  "Move point to the next error in the current buffer and highlight match.
+Prefix arg N says how many error messages to move forwards (or
+backwards, if negative).
+Finds and highlights the source line like \\[next-error], but does not
+select the source buffer."
+  (interactive "p")
+  (next-error-select-buffer (current-buffer))
+  (next-error-no-select n))
+
 (defun previous-error-no-select (&optional n)
   "Move point to the previous error in the `next-error' buffer and highlight match.
 Prefix arg N says how many error messages to move backwards (or
@@ -487,6 +497,16 @@ select the source buffer."
   (interactive "p")
   (next-error-no-select (- (or n 1))))
 
+(defun previous-error-this-buffer-no-select (&optional n)
+  "Move point to the previous error in the current buffer and highlight match.
+Prefix arg N says how many error messages to move forwards (or
+backwards, if negative).
+Finds and highlights the source line like \\[previous-error], but does not
+select the source buffer."
+  (interactive "p")
+  (next-error-select-buffer (current-buffer))
+  (previous-error-no-select n))
+
 ;; Internal variable for `next-error-follow-mode-post-command-hook'.
 (defvar next-error-follow-last-line nil)