# subgroup

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Related to Proper subgroup: Simple group

## sub·group

(sŭb′gro͞op′)
n.
1. A distinct group within a group; a subdivision of a group.
2. A subordinate group.
3. Mathematics A group that is a subset of a group.
tr.v. sub·grouped, sub·group·ing, sub·groups
To divide into subgroups.

## subgroup

(ˈsʌbˌɡruːp)
n
1. a distinct and often subordinate division of a group
2. (Mathematics) a mathematical group whose members are members of another group, both groups being subject to the same rule of combination
Collins English Dictionary – Complete and Unabridged, 12th Edition 2014 © HarperCollins Publishers 1991, 1994, 1998, 2000, 2003, 2006, 2007, 2009, 2011, 2014

## sub•group

(ˈsʌbˌgrup)

n.
1. a subordinate group.
2. Math. a subset of a group that is closed under the group operation and in which every element has an inverse in the subset.
[1835–45]
ThesaurusAntonymsRelated WordsSynonymsLegend:
 Noun 1 subgroup - a distinct and often subordinate group within a groupgroup, grouping - any number of entities (members) considered as a unitbench - the reserve players on a team; "our team has a strong bench" 2 subgroup - (mathematics) a subset (that is not empty) of a mathematical groupmath, mathematics, maths - a science (or group of related sciences) dealing with the logic of quantity and shape and arrangementmathematical group, group - a set that is closed, associative, has an identity element and every element has an inverse
Based on WordNet 3.0, Farlex clipart collection. © 2003-2012 Princeton University, Farlex Inc.
Translations
podgrupa
subgrupo
delgruppundergrupp

## subgroup

[ˈsʌbgruːp] N
Collins Spanish Dictionary - Complete and Unabridged 8th Edition 2005 © William Collins Sons & Co. Ltd. 1971, 1988 © HarperCollins Publishers 1992, 1993, 1996, 1997, 2000, 2003, 2005

## subgroup

sub-group [ˈsʌbgruːp] n
Collins English/French Electronic Resource. © HarperCollins Publishers 2005

## subgroup

[ˈsʌbˌgruːp] nsottogruppo
Collins Italian Dictionary 1st Edition © HarperCollins Publishers 1995
References in periodicals archive ?
Let G = AB be a finite p-group for subgroups A and B such that A is the cyclic group <x> and B is a proper subgroup of G.
If we used L to construct only one element x in A u B then it may have happened with larger probability that C := ([x.sup.G]) is a proper subgroup of A or B.
Since H is a Hall subgroup of G, the hypothesis is satisfied for H and so dl(H) [less than or equal to] [absolute value of cd (H)] by induction argument (Here H is a proper subgroup of G, since q does not divide the order of H).
Theorem 1 The generalized free product of a nilpotent group and a solvable group amalgamated by a proper subgroup of them is not perfect.

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