Problem: The concept of a group arose from the study of polynomial equations, starting with Evariste Galois in the 1830s. After contributions from other fields such as number theory and geometry, the group notion was generalized and firmly established around 1870. Modern group theoryan active mathematical disciplinestudies groups in their own right.a["] To explore groups, mathematicians have devised various notions to break groups into smaller, better-understandable pieces, such as subgroups, quotient groups and simple groups. In addition to their abstract properties, group theorists also study the different ways in which a group can be expressed concretely (its group representations), both from a theoretical and a computational point of view. A theory has been developed for finite groups, which culminated with the classification of finite simple groups announced in 1983.aa["] Since the mid-1980s, geometric group theory, which studies finitely generated groups as geometric objects, has become a particularly active area in group theory.
When was the group notion summed up and solidly settled?
The answer is the following: 1870

Various classes of Vajrayana literature developed as a result of royal courts sponsoring both Buddhism and Saivism. The Manjusrimulakalpa, which later came to classified under Kriyatantra, states that mantras taught in the Saiva, Garuda and Vaisnava tantras will be effective if applied by Buddhists since they were all taught originally by Manjushri. The Guhyasiddhi of Padmavajra, a work associated with the Guhyasamaja tradition, prescribes acting as a Saiva guru and initiating members into Saiva Siddhanta scriptures and mandalas. The Samvara tantra texts adopted the pitha list from the Saiva text Tantrasadbhava, introducing a copying error where a deity was mistaken for a place.
Mantras taught in the Saiva, Garuda, and Vaisnava tantra will be effective if applied by who?
Buddhists

Input: Freemasonry
Regularity is a concept based on adherence to Masonic Landmarks, the basic membership requirements, tenets and rituals of the craft. Each Grand Lodge sets its own definition of what these landmarks are, and thus what is Regular and what is Irregular (and the definitions do not necessarily agree between Grand Lodges). Essentially, every Grand Lodge will hold that its landmarks (its requirements, tenets and rituals) are Regular, and judge other Grand Lodges based on those. If the differences are significant, one Grand Lodge may declare the other "Irregular" and withdraw or withhold recognition.

What concept is based on adherence to Masonic Landmarks, basic membership requirements, and tenets and rituals of the craft?
Output: Regularity

Input: Article: Protestants can be differentiated according to how they have been influenced by important movements since the Reformation, today regarded as branches. Some of these movements have a common lineage, sometimes directly spawning individual denominations. Due to the earlier stated multitude of denominations, this section discusses only the largest denominational families, or branches, widely considered to be a part of Protestantism. These are, in alphabetical order: Adventist, Anglican, Baptist, Calvinist (Reformed), Lutheran, Methodist and Pentecostal. A small but historically significant Anabaptist branch is also discussed.

Now answer this question: What do some branches share in common?

Output: lineage

Article: The majority of insects hatch from eggs. The fertilization and development takes place inside the egg, enclosed by a shell (chorion) that consists of maternal tissue. In contrast to eggs of other arthropods, most insect eggs are drought resistant. This is because inside the chorion two additional membranes develop from embryonic tissue, the amnion and the serosa. This serosa secretes a cuticle rich in chitin that protects the embryo against desiccation. In Schizophora however the serosa does not develop, but these flies lay their eggs in damp places, such as rotting matter. Some species of insects, like the cockroach Blaptica dubia, as well as juvenile aphids and tsetse flies, are ovoviviparous. The eggs of ovoviviparous animals develop entirely inside the female, and then hatch immediately upon being laid. Some other species, such as those in the genus of cockroaches known as Diploptera, are viviparous, and thus gestate inside the mother and are born alive.:129, 131, 134135 Some insects, like parasitic wasps, show polyembryony, where a single fertilized egg divides into many and in some cases thousands of separate embryos.:136137 Insects may be univoltine, bivoltine or multivoltine, i.e. they may have one, two or many broods (generations) in a year.

Question: Chorion is another word for what?
Ans: shell

Input: States of Germany
A new delimitation of the federal territory has been discussed since the Federal Republic was founded in 1949 and even before. Committees and expert commissions advocated a reduction of the number of states; academics (Rutz, Miegel, Ottnad etc.) and politicians (Doring, Apel, and others) made proposals some of them far-reaching for redrawing boundaries but hardly anything came of these public discussions. Territorial reform is sometimes propagated by the richer states as a means to avoid or reduce fiscal transfers.

What have experts advocated in regards to delimitation?
Output:
a reduction of the number of states