Will I be able to complete Inferno without a group?

Solution 1:

Yes, the game is designed around being a single player game with the added option of multiplayer.

That being said a coordinated team will do better due to being able to combine different classes together. This is from a video where Jay Wilson gives tips for inferno mode.

Update: First person to beat Diablo on Inferno did it solo, so it is definitely possible. source

Solution 2:

Yes, it has been stated by Jay Wilson of Blizzard that Inferno will be soloable, and yes, being in a group will make it easier:

Many players are discussing about the Inferno Difficulty since Diablo 2’s Hell just had reduced resistances and that was it. Will there be any type of special feature just for the inferno mode? Also can you solo it?

It will be a lot different from Hell mode in Diablo 2, such as a monster creating a wall to stop the player from fleeing from the monster or blocking off ranged attacks with the use of the wall. The AI will move significantly different also you will be able to solo it even though the difficulty will be a bit easier with co-op it is not a must.