mark-end-of-sentence does what you request. It's not bound to a key by default, but you can bind it to one.
C-h f mark-end-of-sentence tells you:
mark-end-of-sentence is an interactive compiled Lisp function in
Put mark at end of sentence. Arg works as in
If this command is repeated, it marks the next
ARG sentences after the
ones already marked.
You can find this command by asking
C-h a) for commands related to "mark" and "sentence":
C-h a mark sentence.
Commands that select text often have the word
mark in their names, as selecting is about setting the mark at one end of the thing you're selecting (the end opposite point).
Library Thing-At-Point Commands (
thing-cmds.el) has generic command
select-things (aliased to the name
mark-things), to select successive THINGs of any kind that has an associated
If the region isn't active then you're prompted for the type of THING to use.
If the region is active, you aren't prompted, and the last-used type of THING is used again. On consecutive uses of
mark-thing, the region is active, so you aren't prompted, and the region is extended to successive things of the same type.
This is true even if the region is empty, so you can just hit
C-SPC to set mark and activate an empty region, then use
mark-thing to select successive things of the last type used.
thgcmd-bind-keys (interactively or in your init file) binds
select-things. (Vanilla Emacs binds