View source for Young subgroup

Let <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/y/y099/y099080/y0990801.png" /> be a partition of <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/y/y099/y099080/y0990802.png" /> into <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/y/y099/y099080/y0990803.png" /> disjoint subsets. Then the corresponding Young subgroup of <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/y/y099/y099080/y0990804.png" />, the symmetric group on <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/y/y099/y099080/y0990805.png" /> letters, is the subgroup

<table class="eq" style="width:100%;"> <tr><td valign="top" style="width:94%;text-align:center;"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/y/y099/y099080/y0990806.png" /></td> </tr></table>

where <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/y/y099/y099080/y0990807.png" />. Sometimes only the particular cases

<table class="eq" style="width:100%;"> <tr><td valign="top" style="width:94%;text-align:center;"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/y/y099/y099080/y0990808.png" /></td> </tr></table>

are meant where <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/y/y099/y099080/y0990809.png" />, where <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/y/y099/y099080/y09908010.png" /> and <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/y/y099/y099080/y09908011.png" /> is a partition of the natural number <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/y/y099/y099080/y09908012.png" />, i.e. <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/y/y099/y099080/y09908013.png" />, <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/y/y099/y099080/y09908014.png" />.

====References====
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  G.D. James,   "The representation theory of the symmetric groups" , Springer  (1978)  pp. 13</TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top">  A. Kerber,   "Representations of permutation groups" , '''I''' , Springer  (1971)  pp. 17</TD></TR></table>