Can a company buy other company's shares?

yes, many times as part of a "hostile takeover".

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often a subsidiary company will be partially owned by the parent, the parent may retain 51 percent of the stock to retain control. In other cases a company may spin off a division that doesn't fit their plans and make it a stand alone company and own a minority stake.

Sometimes a hostile takeover will be attempted by purchasing and/or controlling a large percentage of shares and affecting who is on the board of directors and other company policies.