specifically group theory, given a prime number p, a p-group is a group in which the order of every element is a power of p. That is, for each element g of a p-group...

mathematics, in the field of group theory, especially in the study of p-groups and pro-p-groups, the concept of powerful p-groups plays an important role....

A&P Group Ltd is the largest ship repair and conversion company in the UK, with three shipyards located in Hebburn, Middlesbrough and Falmouth. The company...

Information". A. P. Moller - Maersk Group A/S. Archived from the original on 8 February 2013. Retrieved 10 January 2013. "Maersk Line - About Us". A. P. Møller...

In mathematics, a pro-p group (for some prime number p) is a profinite group G {\displaystyle G} such that for any open normal subgroup N ◃ G {\displaystyle...

P&T Group (Chinese: 巴馬丹拿), formerly known as Palmer and Turner Hong Kong (Chinese: 公和洋行; "Kung Wo Yeung Hong"), is an architectural firm in Hong Kong...

simple groups. For a prime number p {\displaystyle p} , a Sylow p-subgroup (sometimes p-Sylow subgroup) of a group G {\displaystyle G} is a maximal p {\displaystyle...

specifically in group theory, the Prüfer p-group or the p-quasicyclic group or p∞-group, Z(p∞), for a prime number p is the unique p-group in which every...

other than the identity subgroup, is a cyclic group of order a fixed prime number p. A Tarski monster group is necessarily simple. It was shown by Alexander...

specifically group theory, finite groups of prime power order p n {\displaystyle p^{n}} , for a fixed prime number p {\displaystyle p} and varying integer...

mathematical finite group theory, the concept of regular p-group captures some of the more important properties of abelian p-groups, but is general enough...

specifically in the field of group theory, a solvable group or soluble group is a group that can be constructed from abelian groups using extensions. Equivalently...

P was an American alternative rock band formed in early 1993 by Butthole Surfers frontman Gibby Haynes (vocals), actor Johnny Depp (guitar/bass), actor...

finite group theory, a p-stable group for an odd prime p is a finite group satisfying a technical condition introduced by Gorenstein and Walter (1964, p.169...

Tea Company or A&P supermarket chain A & P Food Stores Building, St. Louis, Missouri, US A&P Canada, former supermarket chain A&P Group, a ship repair company...

the group F p × {\displaystyle \mathbb {F} _{p}^{\times }} is cyclic for prime p {\displaystyle p} : for example, if ⁠ p = 5 {\displaystyle p=5} ⁠,...

ABP Group (Ananda Bazar Patrika) is an Indian media conglomerate headquartered in Kolkata, West Bengal. It was established in 1922. The company in recent...

The M. P. Birla Group is an Indian industrial group named after Madhav Prasad Birla. It has business interests in cement, cables, jute goods and guar gum...

In mathematics, a p-constrained group is a finite group resembling the centralizer of an element of prime order p in a group of Lie type over a finite...

In mathematics, specifically group theory, Cauchy's theorem states that if G is a finite group and p is a prime number dividing the order of G (the number...

In group theory, the quaternion group Q8 (sometimes just denoted by Q) is a non-abelian group of order eight, isomorphic to the eight-element subset {...

space, forming the abelian Lie group of spacetime translations (P); rotations in space, forming the non-abelian Lie group of three-dimensional rotations...

C_{G}(O_{p',p}(G)/O_{p'}(G))\subseteq O_{p',p}(G)} . Every nilpotent group is p-nilpotent, and every p-nilpotent group is p-soluble. Every soluble group is p-soluble...

In mathematics, the indefinite orthogonal group, O(p, q) is the Lie group of all linear transformations of an n-dimensional real vector space that leave...

groups are the additive groups of p {\displaystyle p} -adic integers and the Galois groups of infinite-degree field extensions. Every profinite group...

of p-toluenesulfonic acid, TsO−M+ (e.g., sodium p-toluenesulfonate), or it may refer to esters of p-toluenesulfonic acid, TsOR (R = organyl group). For...

} where φ ( p k ) = φ ( 2 p k ) = p k − p k − 1 . {\displaystyle \varphi (p^{k})=\varphi (2p^{k})=p^{k}-p^{k-1}.} By definition, the group is cyclic if...

voice, and activism. At the age of 15, Pink formed the short-lived girl group Choice, who signed with LaFace Records in 1995, although they disbanded...

free group F n {\displaystyle F_{n}} has ( p n − 1 ) / ( p − 1 ) {\displaystyle (p^{n}-1)/(p-1)} subgroups of index p. The infinite dihedral group has...

In mathematics, the Klein four-group is an abelian group with four elements, in which each element is self-inverse (composing it with itself produces...