* In elementary arithmetic, the set of integers, Z, considered as a group under addition, has a unique nontrivial automorphism: negation.

Xylenol has two methyl groups in addition to the hydroxyl group, and, for this structure, 6 isomers exist.

; Metropolitan bishop: A metropolitan bishop is an archbishop in charge of an ecclesiastical province, or group of dioceses, and in addition to having immediate jurisdiction over his own archdiocese, also exercises some oversight over the other dioceses within that province.

The group that finally overthrew President Patassé consisted of – in addition to Bozizé's own rebels – 100 soldiers from Chad's Military.

In addition, other assaults, robbery, tiger kidnapping, extortion, fuel laundering and smuggling were undertaken by the group.

In addition to igniting spontaneously in air, it reacts explosively with water even at low temperatures, more so than other members of the first group of the periodic table.

If the addition of a functional group takes place at the less substituted carbon atom of the double bond, then the electrophilic substitution with acids is not possible.

While the addition to the electron-rich alkenes and alkynes is mainly electrophilic, the nucleophilic addition plays an important role for the carbon-heteroatom multiple bonds, and especially its most important representative, the carbonyl group.

During his recovery from a heart attack late in 1955, he huddled with his closest advisors to evaluate the GOP's potential candidates ; the group, in addition to his doctor, concluded a second term was well advised, and he announced in February 1956 he would run again.

These age groups roughly correspond to those standardized by FINA, with the addition of a youngest age group for divers 9 and younger, Group E, which does not compete nationally and does not have a tower event ( although divers of this age may choose to compete in Group D ).

This led to the addition of the number sign (#, sometimes called ' octothorpe ,' ' pound ' or ' diamond ' in this context-' hash ' or ' gate ' in the UK ) and asterisk or " star " (*) keys as well as a group of keys for menu selection: A, B, C and D. In the end, the lettered keys were dropped from most phones, and it was many years before these keys became widely used for vertical service codes such as * 67 in the United States of America and Canada to suppress caller ID.

* If we think of as the group of real numbers under addition, then the direct product still consists of.

Additive notation is typically used when numerical addition or a commutative operation other than multiplication interprets the group operation ;

Intuitively, a field is a set F that is a commutative group with respect to two compatible operations, addition and multiplication, with " compatible " being formalized by distributivity, and the caveat that the additive identity ( 0 ) has no multiplicative inverse ( one cannot divide by 0 ).

The most common way to formalize this is by defining a field as a set together with two operations, usually called addition and multiplication, and denoted by + and ·, respectively, such that the following axioms hold ; subtraction and division are defined implicitly in terms of the inverse operations of addition and multiplication :< ref group =" note "> That is, the axiom for addition only assumes a binary operation The axiom of inverse allows one to define a unary operation that sends an element to its negative ( its additive inverse ); this is not taken as given, but is implicitly defined in terms of addition as " is the unique b such that ", " implicitly " because it is defined in terms of solving an equation — and one then defines the binary operation of subtraction, also denoted by "−", as in terms of addition and additive inverse.

Her personal letters to leaders of the Revolution influenced policy ; in addition, she often hosted political gatherings of the Brissotins, a political group which allowed women to join.

For example, the cyclic group of addition modulo n can be obtained from the integers by identifying elements that differ by a multiple of n and defining a group structure that operates on each such class ( known as a congruence class ) as a single entity.

In addition, Hayek attracted an exceptionally able group of students who were dedicated to a libertarian ideology.

In addition to his cosmological writings, Bruno also wrote extensively on the art of memory, a loosely organized group of mnemonic techniques and principles.

The networks for military communications are one of the best examples of networks which not only must be changed with the changes in objectives but also must be changed with the addition of new machines of war.

Besides showing no inclination, apparently, to absent himself from his native region even for short periods, and in addition writing a shelf of books set in the region, he has handled in those books an astonishingly complete list of matters which have been important in the South during the past hundred years.

There was much sickness in the corps, and the men were, in addition, without the clothing, shoes, and blankets needed for the winter weather.

In addition, there are many areas of the human situation besides the impact of science and technology which are examined, for science-fiction dystopias often extrapolate political, social, economic tendencies only indirectly related to science and technology.

In addition, he said, he has answered more than 400 messages of congratulations which led him to the comment that he himself had decided he wouldn't send another congratulatory message for the rest of his life.

Warren and White each carried, in addition to their own weapons and ammo, a box of ammo for the ROK's machine gun.

In addition to the regular schedule, advertisements were run for maximum impact in special editions of the New York Times, Boston Herald, American Banker, Electronic News and, for local promotion, the Providence Sunday Journal.

In addition to maintaining a permanent central file of illustrations of diseases, wounds, and injuries of military importance, it provides facilities for clinical photography, photomicrography, and medical arts, and operates a printing plant, by permission of Congressional Committee, for publication of an `` Atlas of Tumor Pathology ''.

In addition to the basic programs in wavelength standards, spectroscopy, solid state physics, interactions of the free electron and atomic constants which are necessary to provide the foundation for technological progress, the Bureau has strengthened its activities in laboratory astrophysics.

and ( 3 ) research, demonstrations, training and traineeships for vocational rehabilitation -- and in addition for short-term training and instruction.

It stipulates, in addition, that all amounts remaining as a result of imposing the `` ceiling '', and not used for insuring the `` floor '', be redistributed to those States still below their maximums.

In addition, petitioner has failed to show any particular need for the report and notes.

In addition, by starting the Peace Corps now we will be able to begin training young men and women for overseas duty this summer with the objective of placing them in overseas positions by late fall.

In addition to its major effort on fuel cells, Patterson Moos Research Division is continuing to carry on research in other fields, both under contract for the Defense Department, other government agencies and for our own account.

In addition to expenditures on the Warwick plant, we have invested approximately $1,961,000 for machinery and equipment at Cranston, and for new machinery, plant and equipment at Leesona-Holt, Limited.

In addition, Blue Cross coverage for all employees and their dependents was extended to provide the full cost of semi-private hospital accommodations.

In addition to direct salaries and wages, the Company paid or accrued during the year the following amounts for the benefit of employees:

In addition to the three major original equipment segments of the electronics business, the steady growth in the market for replacement parts continues year by year.

Big Magnum calibers appeared in the Remington line for 1961, with the addition of the and to the list of Model 725's.

-- In addition to its recreation interests, water is needed for drinking, sanitation, and irrigation.

* In addition, Finnish, a Baltic-Finnic language, has calqued the Swedish term as Itämeri " East Sea ", disregarding the geography ( the sea is west of Finland ), though understandably since Finland was a part of Sweden from the Middle Ages until 1809.

In addition to Egyptian programming, the Middle East Broadcast Company, a Saudi television station transmitting from London ( MBC ), Arab Radio and Television ( ART ), Al-Jazeera television, and other Gulf stations as well as Western networks such as CNN and BBC, provide access to more international programs to Egyptians who own satellite receivers.

In addition, Gesta Danorum offers singular reflections on European affairs in the High Middle Ages from a unique Scandinavian perspective, supplementing what has been handed down by historians from Western and Southern Europe.

Czech houfnice is derived, through the addition of the suffix-nice, from the word houf, " crowd ", suggesting the cannon's use against massed enemies, and houf is in turn a borrowing from the Middle High German word Hūfe or Houfe ( modern German Haufen ), meaning " heap ".

In addition to their promised allegiance to the other, Louis and Charles pledged their solidarity to oppose their eldest brother Lothair, ruler of Middle Francia and, nominally, emperor of all the Carolingian Empire Frankish kingdoms as well as Holy Roman Emperor.

It was not until the Gamal Abdel Nasser era that Arab nationalism ( in addition to Arab socialism ) became a state policy and a means with which to define Egypt's position in the Middle East and the world, usually articulated vis-à-vis Zionism in the neighboring Jewish state of Israel.

By the end of the 18th century, in addition to the trivium and quadrivium of the Middle Ages, the definition of a classical education embraced study of literature, poetry, drama, philosophy, history, art, and languages.

In addition to revolutionising the free media in the Middle East and indeed the rest of the world, the Qatar funded Qatar Airways has gone on an aggressive expansion, which also competes with nearby Emirates Airline, to reach more destinations and serve more passengers.

In addition the Rotterdam office has a number of activities in the Middle East including office and residential towers and master plans in Dubai, three master plans in Ras-Al-Khaimah and several public buildings in Qatar.

In addition to these economic sectors, overseas employment contributes highly in foreign exchange, 90 % of expatriate Sri Lankans reside in the Middle East.

In addition to this there are many Sinhalese, who reside in the above mentioned countries and countries in the Middle East, Southeast Asia and Europe, temporarily in connection with employment and education.

In most of the writing systems of the Middle East, it is usually only the consonants of a word that are written, although vowels may be indicated by the addition of various diacritical marks.

The Papacy in the Late Middle Ages played a major temporal role in addition to its spiritual role.

In addition to its Pittsburgh campus, Carnegie Mellon has a branch campus in the Middle East, Carnegie Mellon University in Qatar, which offers a full undergraduate curriculum with degree programs in computer science, business administration and information systems.

In addition, many early sword and sorcery writers, such as Robert E. Howard and Clark Ashton Smith, were heavily influenced by the Middle Eastern tales of the Arabian Nights, whose stories of magical monsters and evil sorcerers were a major influence on the genre-to-be.

In addition, Belle Isle Enterprise Middle School in OKCPS was named the top middle school in the state according to the Academic Performance Index, and recently received the Blue Ribbon School Award, in 2004 and again in 2011.

In addition, other terms and phrases associated with " courtliness " and " love " are common throughout the Middle Ages.

In addition, some of the greatest theologians of the High Middle Ages, Thomas Aquinas and Robert Grosseteste, were products of the medieval university.

Middle Eastern countries within the sphere of Soviet influence — Egypt, Syria, Iraq, Afghanistan and Palestinian fighters — have received them in addition to other more modern arms.

In addition to scheduled routes inherited from BUA, it launched scheduled services to Europe, North and West Africa, North America as well as the Middle and Far East during the 1970s and ' 80s.

In addition to the superpower states, international broadcast services grew in Europe and the Middle East.

In addition, approximately 500 students in grades Pre-K through 8 attend Oakman Elementary / Middle School.

A new high school on the property now occupied by Clifton Middle School was erected in 1905, and in 1912 was greatly expanded by the addition of new buildings.

In addition, there is also one middle school-Miller Creek Middle School Panthers, a California Distinguished School.