When the Prophet (may Allah's peace and blessings be upon him) prayed, he used to spread out his hands until the whiteness of his armpits would be visible

This posture, in which one keeps his upper arms away from his sides, is recommended in Sujūd.
It is not permissible for the one praying behind the Imam to adopt the Mujāfāh posture (keeping the arms quite distant from the sides) if this annoys the one praying next to him.
Mujāfāh in Sujūd has many rationales and benefits, some of which are: displaying activeness and interest in prayer; and when resting on all of the body parts involved in Sujūd, each part will take its share of worship. It was also said: The rationale behind this is that it resembles humility more and enables one to place his forehead and nose on the ground in a more proper manner, and it also allows each body part to be involved apart from other parts.