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Page "The Sandbaggers" ¶ 21
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Burnside's and personal
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 and professional life come together in Sir Geoffrey Wellingham ( Alan MacNaughtan ), who is both Burnside's former father-in-law and the Permanent Undersecretary of State at the Foreign and Commonwealth Office that oversees SIS.

Burnside's and assistant
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.

Burnside's and has
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.
Burnside's theorem has long been one of the best-known applications of representation theory to the theory of finite groups, though a proof avoiding the use of group characters was published by D. Goldschmidt around 1970.

Burnside's and with
Hooker embarked on a reorganization of the army, doing away with Burnside's grand division system, which Hooker considered unwieldy ; he also no longer had sufficient senior officers on hand that he could trust to command multi-corps operations.
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.
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.
( 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.
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.
Adding a third floor to Burnside's structure it formed the arch with its towers and its oriel window and extended in two reaches to the south, the further slightly set back from the street.
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.
Along with Burnside's old IX Corps, which had been sent west with him after Fredericksburg, it was to maintain a primarily defensive position in Eastern Tennessee and Kentucky.

Burnside's and her
`` I'm General Burnside's horse, upside down '', Arlene said, sort of gaspingly, for her: even she had to breathe kind of funny when she was in that position.

Burnside's and is
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.
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:
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 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.
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

Burnside's and him
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.

Burnside's and .
One day, the children had wanted to get up onto General Burnside's horse.
She made General Burnside's horse's belly do so funny when it was upside down.
It was General Burnside's horse running in a circle.
* 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.
This follows from Burnside's p-q theorem.
Predictably, Burnside's purge went nowhere, and he offered President Abraham Lincoln his resignation from command of the Army of the Potomac.
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.
With Burnside's departure, Maj. Gen. William B. Franklin left as well.
Then he would rapidly shift his army southeast and cross the Rappahannock River to Fredericksburg, hoping that Robert E. Lee would sit still, unclear as to Burnside's intentions, while the Union Army made a rapid movement against Richmond, south along the Richmond, Fredericksburg and Potomac Railroad from Fredericksburg.
The Union Army was in a position reminiscent of the one Longstreet had harnessed at Fredericksburg to defeat Burnside's assault.
After weeks of preparation, on July 30 the Federals exploded a mine in Maj. Gen. Ambrose E. Burnside's IX Corps sector, blowing a gap in the Confederate defenses of Petersburg, Virginia.
Finally, Lt. Col. Henry Pleasants, commanding the 48th Pennsylvania Infantry of Maj. Gen. Ambrose E. Burnside's IX Corps, offered a novel proposal to break the impasse.

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