Claim: Fredericksburg Union order of battle had two divisions, one of which was run by Alpheus S. Williams(September 20, 1810 – December 21, 1878).
Evidence: The following Union Army units and commanders fought in the Battle of Fredericksburg of the American Civil War. Order of battle compiled from the army organization during the campaign. The Confederate order of battle is listed separately. Division Brigade Regiments and Others MG Henry Warner Slocum Escort 12th Illinois Cavalry, Company A: Cpt P. E. Fisher First Division
BG Alpheus S. Williams 1st Brigade
Col Joseph F. Knipe 2nd Brigade
BG Thomas L. Kane 3rd Brigade
BG John K. Murphy Artillery
Cpt Robert H. Fitzugh Cavalry Second Division
BG John W. Geary 1st Brigade
BG Charles Candy 2nd Brigade
Col Joseph M. Sudsburg 3rd Brigade
BG George S. Greene Artillery
Maj L. Kieffer Cavalry 
At the outbreak of the Civil War in 1861, Williams was involved in training the first army volunteers in the state. He was promoted to brigadier general of volunteers on May 17, 1861. He then assumed division command in the V Corps of the Army of the Potomac, as of March 13, 1862. Williams' division missed the next major battle for the Army of the Potomac, the Battle of Fredericksburg, because it was engaged in defending the Potomac River in the Reserve. 
MG Ambrose Burnside, Commanding MG Edwin Vose Sumner MG Darius N. Couch First Division
MG Winfield Scott Hancock Second Division
MG Oliver O. Howard Third Division
MG William H. French Corps Artillery Reserve
Cpt Charles H. Morgan BG Orlando B. Willcox Escort 6th New York Cavalry, Company B: Cpt Hillman A. Hall 6th New York Cavalry, Company C: Cpt William L. Heermance First Division
BG William W. Burns Second Division
BG Samuel D. Sturgis Third Division
BG George W. Getty BG Alfred Pleasonton 1st Brigade
BG John F. Farnsworth MG Joseph Hooker BG George Stoneman First Division
BG David B. Birney Second Division
BG Daniel Sickles Third Division
BG Amiel W. Whipple MG Daniel Butterfield First Division
BG Charles Griffin Second Division
MG George Sykes Third Division
BG Andrew A. Humphreys Cavalry Brigade
BG William W. Averell Artillery MG William B. Franklin Escort 6th Pennsylvania Cavalry: Col Richard H. Rush MG John F. Reynolds Escort 1st Maine Cavalry, Company L: Cpt Constantine Taylor First Division
BG Abner Doubleday Second Division
BG John Gibbon (w)
BG Nelson Taylor Third Division
MG George Meade MG William F. Smith Escort 10th New York Cavalry, Company L: Lt George Vanderbilt 6th Pennsylvania Cavalry, Company I: Cpt James Starr 6th Pennsylvania Cavalry, Company K: Cpt Frederick C. Newhall First Division
BG William T. H. Brooks Second Division
BG Albion P. Howe Third Division
BG John Newton Artillery Cavalry Brigade
BG George D. Bayard (k)
Col David McM. Gregg Further information: Official Records, Series I, Volume XXI, Part 1, BG Julius Stahel First Division
BG Nathaniel C. McLean Second Division
BG Adolph Von Steinwehr Third Division
BG Carl Schurz Unattached