FREQUENTLY USED SYMBOLS

	GROUP (p. 1)
	SUBGROUP (p. 10)
	INDEX of with respect to = number of left (right) cosets (p. 10)
	COMPLEX = subset of a group (p. 19)
	Complex transformed by x = set of all xKx–1 (p. 25)
	NORMALIZER of = group of all x which transform into itself (p. 26)
	CENTRALIZER of = group of all x which are permutable with every element of (p. 50)
	NORMAL SUBGROUP = subgroup which is transformed into itself by all elements (p. 23)
	FACTOR GROUP of over = group of cosets of by (p. 38)
	CENTER OF = group of all elements commuting with every element of (p. 27)
	Group of all INNER AUTOMORPHISMS (transformations) of (p. 48)
	Group of all AUTOMORPHISMS of (p. 48)
A / J	Group of OUTER AUTOMORPHISMS of (p. 48)
Φ	A subgroup of = intersection of with its maximal subgroups (p. 49)
(a, b) = aba–1b–1	COMMUTATOR of a with b (p. 18)
(a, b, c) = (a, (b, c))	(p. 81)
	mutual COMMUTATOR GROUP = group of all (U, V) (p. 81)
	COMMUTATOR GROUP of (p. 67)
	FACTOR COMMUTATOR GROUP (p. 67)
	i-TH DERIVATIVE of (p. 79)
k	degree of METABELIAN group , so that (p. 79)
	DESCENDING CENTRAL SERIES (p. 155) so that
	is the i-th Reidemeister commutator group
	ascending central series (p. 50) so that
	is the i-th center of , hence is the center of
c	Class of the nilpotent group , hence and
	is a SYLOW p-GROUP of (p. 135)
	Normalizer of (p. 135)
	Center (p. 135)
	The minimal number of independent generators of (p. 141)
	(pd−1—1) ... (p — 1) (p. 142)
	p-commutator group = intersection of all normal subgroups with abelian p-factor group (p. 158)
	p-factor commutator group = maximal abelian p-factor group (p. 158)
	Intersections of all normal subgroups with index a power of p (p. 159)
	Maximal p-factor group (p. 159)
∈	means: x is an element of
	means: is a proper subgroup of
	is the sum of the sets and
	is the intersections of and
	means: is a subgroup of
	means: is a normal subgroup of
	means: is a subnormal subgroup of
{, }	or 〈 , 〉 denotes the subgroup generated by the two subgroups , of a group
×	× denotes the direct product of the groups ,
*	* denotes the free product of the groups ,
≤	a ≤ b (b ≥ a or a C b) means: the poset element a is contained in the poset element b
<	a < b means: a ≤ b, but not b ≥ a; also denoted by: a > b
K	a K b means: the lattice element a is Kurosh-invariant in the lattice element b
N	a N b means: a is normal in b
NN	a NN b means: a is subnormal in b
J	a J b denotes the join of a and b
M	a M b denotes the meet of a and b
a/b	denotes the factor lattice of a over b