However, the abstract formalization of the group axioms, detached as it is from the concrete nature of any particular group and its operation, allows entities with highly diverse mathematical origins in abstract algebra and beyond to be handled in a flexible way, while retaining their essential structural aspects.

However, the Prussian and other German armies were delayed for months at the Siege of Metz and the Siege of Paris, due to the greatly increased firepower of the defending infantry, and the principle of detached or semi-detached forts with heavy-caliber artillery.

However, the Treaty of Versailles following World War I restored West Prussia to Poland and made East Prussia an exclave of Weimar Germany, while the Memel Territory was detached and was annexed by Lithuania in 1923.

However, his detached, timid and morose character, his search of perfection frequently made him lose friendships and popularity.

However, by 1843, there was a continuous line of houses, predominantly detached and usually with separate coach houses along the full length of Lower Tulse Hill Road from Brixton to the top of the hill.

However, this would not occur until November 27, 1806, when the territory now encompassing all of the Oranges was finally detached.

However, Desaix, in charge of the force Bonaparte had detached southwards, had hastened his advance and reached a small road junction north of Cascina Grossa ( 3 kilometers west of San Giuliano ).

However, Childers remained detached from the government ; whereas previously, presidents had been briefed by taoisigh once a month, Cosgrave briefed President Childers and his successor, Cearbhall Ó Dálaigh on average once every six months.

However, 30 minutes after issuing his first order, Raglan now changed his mind and issued his second order at 08: 30 – " Eight squadrons of heavy Dragoons to be detached towards Balaclava to support the Turks who are wavering ".

However, it is not widely used in building industrial test and measurement systems for a number of reasons ; for example, USB cables are not industrial grade, are noise sensitive, can accidentally become detached, and the maximum distance between the controller and the device is 30 m. Like RS-232, USB is useful for applications in a laboratory setting that do not require a rugged bus connection.

However, in many single family detached and smaller multiple family housings, a smoke alarm is often powered only by a single disposable battery.

However, this style quickly gave way to the ' modern ' style of detached housing which allowed better motor vehicle access amongst other benefits.

However, in the Scout Association of United Kingdom ( UK ) and some of its overseas branches, the two-finger salute was later replaced by the three-finger salute when they detached from the Jungle theme.

However in the 1890s, with the construction of the Manchester Ship Canal, the basin became detached from the river.

However the axles were hard to install on the chassis while being assembled and would become detached from the lugs on the baseplate if very hard pressure was applied.

However, all evacuee families had a right to receive a small farm, and / or a plot for a detached house or a flat.

However, since the 19th century this urban region has been detached administratively from remaining more rural county.

However, as early as 1887, Dakar was detached from the commune of Gorée and was turned into a commune in its own right.

" However, even though the lyrics ' " hopefulness shriveled into empty promise ", the performance of the song " is emotionally detached from Hopkins ' afflictions " and presents a " sunny soundtrack " for his depression.

However, it is not widely used in building industrial test and measurement systems for a number of reasons ; for example, USB cables are not industrial grade, are noise sensitive, can accidentally become detached, and the maximum distance between the controller and the device is 30 m. Like RS-232, USB is useful for applications in a laboratory setting that do not require a rugged bus connection.

However the office had precedents in the duties and rights held by some officers of the Navarrese dynasty of Castile and León, and Álvar Fáñez or Fortún Sánchez in the Ebro valley performed similar services in detached territories beyond the frontier.

However, politically and administratively speaking, and no matter whether contiguous or detached, the four constituent parts of the Quatre-Vallée province were, from south to north:

However, the relative pronoun in the role of object of the preposition can indeed be that if it is placed at the start of the dependent clause while the preposition is detached from it and located at the end of the clause, as in the above example Jack is the boy that Jenny fell in love with.

However, by the time Europeans started to penetrate the region, Msiri's son Simbi, advancing from the south and forming alliances with the Hemba rulers against incursions from Tippu Tip, had detached Kyombo Mkubwa from the Luba heartland.

However, in the actual assessment of the cutting force by instrumental methods for any thickness of coating a number of spurious effects occur which must be taken into account and which make the measured value larger than the true cutting force indicated by eqn. ( 1 ).

However, the Vandals tried for several decades to force their Arian beliefs on their North African Nicene subjects, exiling Nicene clergy, dissolving monasteries, and exercising heavy pressure on non-conforming Christians.

However, at the base of this crack is a round void called an ampulla which would have functioned to distribute force over a larger surface area, hindering the ability of the " crack " formed by the serration to propagate through the tooth.

However, in some situations, especially when deep behind enemy lines, the actual attack will be carried out by a platoon, a company-sized unit will be deployed to support the attack group, setting up and maintaining a forward patrol harbour from which the attacking force will deploy, and to which they will retire after the attack.

However, with the Franco-Bavarian commanders reluctant to fight until their numbers were deemed sufficient, the Duke enacted a policy of plundering in Bavaria designed to force the issue.

However, the Luftwaffe was a broadly based force with no constricting central doctrine, other than its resources should be used generally to support national strategy.

However, Nigeria never ratified the agreement, while Cameroon regarded it as being in force.

However, the explanation of this curvature involves centrifugal force for all observers with the exception of a truly stationary observer, who finds the curvature is consistent with the rate of rotation of the water as they observe it, with no need for an additional centrifugal force.

However, he realized that his equations permitted the introduction of a constant term which could counteract the attractive force of gravity on the cosmic scale.

However in Daoism it refers more often to a meta-physical term that describes a force that encompasses the entire universe but which cannot be described nor felt.

However, if they showed treasonous inclinations, the Emperor did punish them with just force, as in the case of Polybius and Pallas ' brother, Felix.

However, there also are nonphysical forms of coercion, where the threatened injury does not immediately imply the use of force.

However, an Assyrian king Ashur-uballit II held out at the Assyrian city of Harran, resisting until 605 BC, when the remnants of the Assyrian Army and an Egyptian force were defeated at Karchemish.

However, the mystique of the cavalry is such that the name has been introduced for what was always a mechanised force.

However, the anti-terrorist measures of it remained in force.

However, it did not emerge as a formidable force until 1991, when the elderly LY members elected from the mainland provinces in 1948 retired.

However, the Dalek force is destroyed by the Doctor, and Davros is captured and imprisoned by the humans in suspended animation, before being taken to Earth to face trial.

However, limited funds hinder any major acquisitions and the chances of maintaining a strong force within the Pacific Ocean.

However, some emulsions would never coalesce under normal gravitational force, but will under higher g forces.

However at least three other factors work against dialects, namely the centripetal force of the Fundamento, the unifying influence of the Plena Vortaro and its successors, which exemplified usage from the works of Zamenhof and leading writers, and the transnational ambitions of the speech community itself.

However, the force is defeated, and Godzilla proceeds on his original course.

However, their velocities are too large for them to remain gravitationally bound by their mutual attractions, implying the presence of either an additional invisible mass component, or an additional attractive force besides gravity.

However, the invasion of the Macriani forced him to dispatch Aureolus with a large force against them, leaving him with insufficient troops.