The personal price he pays in that episode sparks an obsession with the safety of his Sandbaggers and the survival of the special section in subsequent episodes, contributing to Burnside's gradual psychological unravelling and the series ' unresolved cliffhanger ending.

Burnside's personal assistant Diane Lawler ( Elizabeth Bennett ) has regular clashes with her boss but is fiercely loyal to him.

Although substantial changes ( such as forward passing ) were still to come, modern Canadian football would ultimately evolve from John Thrift Meldrum Burnside's code.

Thus if G is any finitely generated group of exponent n, then G a homomorphic image of B ( m, n ), where m is the number of generators of G. Burnside's problem can now be restated as follows:

From left to right: Jeff Ross ( Sherman ), Willie Caine ( Lonnen ) and Neil Burnside ( Marsden ) in Burnside's office.

after Burnside's original proof ), and a theorem of Richard Brauer and Michio Suzuki stating that a finite simple group cannot have a generalized quaternion group as its Sylow 2 subgroup.

Both " Left Grand Division " commander Maj. Gen. William B. Franklin, who vowed that he would not serve under Hooker, and II Corps commander Maj. Gen. Edwin Vose Sumner were relieved of command, on Burnside's recommendation, in the same order appointing Hooker to command.

The central part of Burnside's group theory work was in the area of group representations, where he helped to develop some of the foundational theory, complementing and sometimes competing with the work of Frobenius, who began the subject in the 1890s.

Actor Ray Lonnen, who played Sandbagger Willie Caine, has indicated in correspondence with fans that there were plans for a follow-up season in which his character, using a wheelchair, had taken over Burnside's role as Director of Special Operations.

The attack on Burnside's conjecture was started by, who studied CA groups ; these are groups such that the Centralizer of every non-trivial element is Abelian.

Later joint work of Ol ' shanskii and Ivanov established a negative solution to an analogue of Burnside's problem for hyperbolic groups, provided the exponent is sufficiently large.

The full solution to Burnside's problem in this form is not known.

A famous class of counterexamples to Burnside's problem is formed by finitely generated non-cyclic infinite groups in which every nontrivial proper subgroup is a finite cyclic group, the so-called Tarski Monsters.

In 1982 Ol ' shanskii was able to strengthen his results to establish existence, for any sufficiently large prime number p ( one can take p > 10 < sup > 75 </ sup >) of a finitely generated infinite group in which every nontrivial proper subgroup is a cyclic group of order p. In a paper published in 1996, Ivanov and Ol ' shanskii solved an analogue of Burnside's problem in an arbitrary hyperbolic group for sufficiently large exponents.

This cumbersome arrangement contributed to his slowness in attacking and crossing what is now called " Burnside's Bridge " on the southern flank of the Union line.

Burnside is also remembered for the formulation of Burnside's problem

Burnside's lemma, sometimes also called Burnside's counting theorem, the Cauchy-Frobenius lemma or the orbit-counting theorem, is a result in group theory which is often useful in taking account of symmetry when counting mathematical objects.

Consequently, this lemma is sometimes referred to as the lemma that is not Burnside's.

( This is the first edition ; the introduction to the second edition contains Burnside's famous volte face regarding the utility of representation theory.

Burnside's demeanour towards his superior is insubordinate and sometimes even hostile.

Novikov is known for his work on combinatorial problems in group theory: the word problem for groups, and Burnside's problem.

The creek is noted for numerous well-preserved stone arch bridges dating to the 19th century that still traverse the creek, the most famous of which is the Burnside's Bridge in the Antietam National Battlefield.

In mathematics, Burnside's theorem in group theory states that if G is a finite group of order

( which concerns the question of bounding the size of a group if there are fixed bounds both on the order of all of its elements and the number of elements needed to generate it ) and for Burnside's lemma ( a formula relating the number of orbits of a permutation group acting on a set with the number of fixed points of each of its elements ) though the latter had been discovered earlier and independently by Frobenius and Cauchy.

With both bridges destroyed, Burnside's soldiers had to be ferried across the river by the gunboats.

However, his indiscretion in communicating to Lincoln directly about Burnside's shortcomings, compounded by the fact that Smith was a close friend of out-of-favor Maj. Gen. George B. McClellan, resulted in his losing both his corps command and his rank ; the Senate failed to confirm his nomination to major general, which expired on March 4, 1863.

General Reno was in command of both divisions in Burnside's absence.

Burnside's former command, the IX Corps, was transferred to the Virginia Peninsula, a movement that prompted the Confederates to detach troops from Lee's army under Lt. Gen. James Longstreet, a decision that would be consequential in the upcoming campaign.

* 1862 – American Civil War: President Abraham Lincoln approves General Ambrose Burnside's plan to capture the Confederate capital at Richmond, Virginia, leading to the Battle of Fredericksburg.

Burnside's plan was to cross the Rappahannock River at Fredericksburg in mid-November and race to the Confederate capital of Richmond before Lee's army could stop him.

The Union Army was in a position reminiscent of the one Longstreet had harnessed at Fredericksburg to defeat Burnside's assault.

On March 11, Brigadier General Ambrose Burnside's command embarked from Roanoke Island to rendezvous with Union gunboats at Hatteras Inlet for an expedition against New Bern.

He approved the plan of Maj. Gen. Ambrose Burnside to plant explosives in a mine shaft dug underneath the Confederate line east of Petersburg, but at the last minute he changed Burnside's plan to lead the attack with a well-trained African-American division that was highly drilled just for this action, instructing him to take a politically less risky course and substitute an untrained and poorly led white division.

Burnside's IX Corps, which accompanied the army at the start of Ulysses S. Grant's Overland Campaign, was added later.

Crook led his brigade at the battle of South Mountain and near Burnside's Bridge at the battle of Antietam.

The divisions had been organized in 1861 ( the first, Banks ' Division of the Army of the Potomac, as early as July ) and by January, included 13 such formations in the Army of the Potomac ; two in Western Virginia ; one ( Burnside's ) in Maryland ; one ( Sherman's ) in South Carolina ; five more in the Army of the Ohio ; and one each in Missouri and Tennessee, for a total of 24 ; this total does not include multiple separate brigade-level formations, much less units in garrison at various fortifications and other posts from Maine to California.

In July 1862, Hartranft's men proceeded to Newport News, Virginia, to become part of Burnside's IX Corps, with whom they fought in the Second Battle of Bull Run and at South Mountain.

They also fought at the Battle of Antietam, where Hartranft led its famous charge across Burnside's Bridge, suffering 120 casualties.

Furthermore, Dr. Mary Edwards Walker served as assistant surgeon with General Burnside's Union forces in 1862 and with an Ohio regiment in East Tennessee the following year ; imprisoned in Richmond as a spy, she was eventually released and returned to serve as a hospital surgeon at a women ’ s prisoner-of-war hospital in Louisville, Kentucky.

The Battle of Antietam, by Kurz & Allison, depicting the scene of action at Burnside's Bridge

As a Confederate army under General Braxton Bragg besieged Union forces at Chattanooga, Tennessee, a detachment under the command of Lt. Gen. James Longstreet, a trusted subordinate of Robert E. Lee, was sent to Knoxville to prevent Burnside's Army of the Ohio from moving in support of Chattanooga.

In early November 1863, Lt. Gen. James Longstreet, with two divisions and about 5, 000 cavalry, was detached from the Confederate Army of Tennessee near Chattanooga, Tennessee, to attack Maj. Gen. Ambrose E. Burnside's Union Department of the Ohio troops at Knoxville.

Potter was wounded at Antietam while participating in Burnside's attack on the Confederate right flank.

Named Chief of Artillery of Maj. Gen. Ambrose Burnside's IX Corps, he served at the battles of South Mountain and Antietam during the Maryland Campaign.