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An abelian group is a set, together with an operation ･ , that combines any two elements and of to form another element of , denoted .The symbol ･ is a general placeholder for a concretely given operation.
Dedekind and Baer have shown (in the finite and respectively infinite order case) that every Hamiltonian group is a direct product of the form G = Q 8 × B × D, where B is an elementary abelian 2-group, and D is a torsion abelian group with all elements of odd order. Dedekind groups are named after Richard Dedekind, who investigated them in ...
A religious order is characterized by an authority structure where a superior general has jurisdiction over the order's dependent communities. An exception is the Order of Saint Benedict which is not a religious order in this technical sense, because it has a system of independent houses, meaning that each abbey is autonomous. However, the ...
In the phrase "holy orders", the word "holy" means "set apart for a sacred purpose". The word "order" designates an established civil body or corporation with a hierarchy, and ordination means legal incorporation into an order. In context, therefore, a group with a hierarchical structure that is set apart for ministry in the Church.
Most use a pre-1970 edition of the Roman Missal, usually 1962 Missal, but some follow other Latin liturgical rites and thus celebrate not the Tridentine Mass but a form of liturgy permitted under the 1570 papal bull Quo primum. The use of a pre-1970 Roman Missal has never been prohibited by the Catholic Church. Despite never being suppressed by ...
Pages in category "Catholic religious orders established in the 16th century" The following 14 pages are in this category, out of 14 total. This list may not reflect recent changes .
Order p 2: There are just two groups, both abelian. Order p 3: There are three abelian groups, and two non-abelian groups. One of the non-abelian groups is the semidirect product of a normal cyclic subgroup of order p 2 by a cyclic group of order p. The other is the quaternion group for p = 2 and a group of exponent p for p > 2.
The Ordo Lectionum Missae (known officially in English as Order of Readings for Mass [1] [2] [3]), commonly referred to as OLM, is the main liturgical lectionary used in the Roman Catholic Church. It contains the designated Scripture readings for the celebration of the Mass of Paul VI , encompassing selections ( pericopes ) from both the Old ...