100 English words for 'For given group G and element g ∈ G, the smallest positive natural number n, if it exists, such that (using multiplicative notation), gⁿ = e, where e is the identity element of G; if no such number exists, the element is said to be of infinite order (or sometimes zero order).'

order

least common multiple

characteristic

primitive root

multifactorial

Fitting subgroup

prime number

finite

well-order

hyperreal

prefundamental

Pisot-Vijayaraghavan number

weird number

Gaussian prime

p-adic ordinal

Turing degree

Blum integer

Cayley's theorem

divisibility sequence

simsun permutation

aleph-nought

aleph-null

aleph-zero

Sierpinski number

amorphous

Waring's problem

Feit-Thompson theorem

Frobenius number

lowest common denominator

lcm

subrepresentation

primitive element

coprime

surreal number

group

Romanov's theorem

subgroup

supremum

lowest common multiple

normal

mathematical group

torsion subgroup

subpower

Listing number

Heegner number

divergent series

pseudointersection

prime

prime quantity

Dickson's conjecture

nilspace

almost all

sporadic group

adjunction

infinity

irreflexive

Schinzel's hypothesis H

Dirichlet series

Bézout's identity

Liouville number

hyperperfect number

natural unit

group object

nonassociative

ordered integral domain

principal ideal

parity

root of unity

zeroless

alternating series

diagonal argument

unity

remainder

quintate

hyperring

uncountable set

Archimedean property

Galileo's paradox

Klein geometry

Proth number

Ax-Kochen theorem

coinitial

formal power series

integer

continuum hypothesis

pigeonhole principle

hypergeometric series

algebraic integer

superior highly composite number

unmultipliable

whole number

terminate

abelian group

Helly family

pseudoinfinite

semisimple

Dedekind cut