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

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

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.

`` 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.

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.

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.

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.

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.

The divide is punctuated by examples of Dublin " sub-culture " stereotypes, with upper-middle class constituents seen as tending towards an accent and demeanour synonymous with the Southside, and working-class Dubliners seen as tending towards characteristics associated with Northside and inner-city areas.

There also exists the rare usage, para con ( demeanour “ towards ”, “ against ”, “ with ”, “ unto ” someone or something ):

He still displays a cold demeanour towards Batman, but toned down, implying that he has fully accepted him as an ally.

Holmes's demeanour is presented as dispassionate and cold.

* The captured Caratacus is exhibited in chains in Claudius ' triumph in Rome, but his dignified demeanour persuades the emperor to spare his life and allow his family to live free in the capital for short period of time.

Little is known of Faith's life or demeanour, but a love letter from Wren survives, which reads, in part:

The seme is generally older and taller, with a stronger chin, shorter hair, smaller eyes, and a more stereotypically masculine, even " macho ", demeanour than the uke.

His cold demeanour is representative of what the sixteenth century thought to be a side-effect of political genius Conversely, Antony ’ s focus is on valour and chivalry, and Antony views the political power of victory as a by-product of both.

This spot is to be reverenced with religious awe and solemnity of demeanour, by those whose affairs lead them to visit it.

* The Black Knight is a moniker given to golfer Gary Player in the 1960s by the media for his penchant for black attire on and off the golf course and for his courteous demeanour.

Because of his long-running television career and eccentric demeanour, Moore is widely recognised and has become a popular public figure.

Adding to the inner complexities of the picture and creating further visual interactions is the male dwarf in the foreground, whose raised hand echoes the gesture of the figure in the background, while his playful demeanour, and distraction from the central action, are in complete contrast with it.

Progressive Architecture commented that “ behind Windsor ’ s seemingly conservative demeanour is a place imbued with the spirit of social reform .”

Her calm, cold demeanour suggests that she too is a mixture of the Queen of Hearts and the Red Queen.

He has capitalised on his tough man image as a footballer and is known as an actor for his aggressive style and intimidating demeanour, often being typecast into roles as coaches, hooligans and violent criminals.

Darren is portrayed to be dumb, uneducated and of a laid back demeanour.

Stockinger is thin and always has a very serious demeanour.

His sleepy demeanour can be misleading-he has an astute mind, considerable leadership qualities and is a talented boxer who is a match for anyone in the form.

Charles is a sporting hero in New Zealand, not only for his achievements but also for his demeanour and philanthropy regarding junior golfers.

In DSM-IV-TR the inhibited form is described as persistent failure to initiate or respond in a developmentally appropriate fashion to most social interactions, as manifest by excessively inhibited, hypervigilant, or highly ambivalent and contradictory responses ( e. g., the child may respond to caregivers with a mixture of approach, avoidance, and resistance to comforting or may exhibit " frozen watchfulness ", hypervigilance while keeping an impassive and still demeanour ).

: Mr Logic: I shall commence by pointing out to you that my demeanour is not one which could be described as nonsensical.

However, due to his emotionless demeanour, he ignores the fact that they are trying to get to the hospital as the lady of the house is in labour.

Lukewarm is a rotund young man with a calm and personable demeanour, who originates from Middlesbrough.

Alliss is known for his charismatic and unique style of commentary, often displaying a witty demeanour.