Equation 677 Database

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Magma f9207699f97a…

magma f9207699f97a
Size
321
Isomorphism class hash
f9207699f97a51c7d29298c41f864a39b5640dce43f7b2c7cd61348bc9f122a9
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 320) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 22:45:07
Display reorder
300,94,161,133,143,68,92,69,159,131,141,160,70,93,132,142,163,96,71,224,226,162,95,72,134,244,239,219,229,135,144,128,156,89,73,138,157,90,74,129,139,158,91,75,130,140,88,155,76,127,137,218,228,77,126,136,87,246,240,223,225,306,307,303,310,287,284,285,286,55,279,53,277,276,278,281,54,283,280,282,297,299,58,296,298,289,291,56,288,290,57,295,293,292,294,265,264,267,50,266,268,271,51,269,270,272,275,52,273,274,263,260,49,261,262,255,252,47,253,254,259,257,48,256,258,320,317,318,319,21,196,37,29,221,208,241,249,38,28,195,107,20,39,209,234,199,108,40,32,197,19,109,41,30,110,18,198,42,31,43,192,24,111,35,193,22,112,44,33,194,23,113,45,34,27,191,114,212,211,25,190,115,46,36,26,248,242,213,210,302,316,312,314,151,170,122,14,6,149,4,168,120,12,169,5,150,121,13,173,154,1,125,17,171,152,3,123,15,2,153,172,124,16,117,166,146,205,10,231,147,204,118,207,167,148,8,119,11,145,165,0,243,206,245,230,236,222,237,227,164,7,116,9,305,308,309,311,178,104,83,183,64,179,62,102,84,181,103,63,177,82,182,201,174,60,200,186,105,175,61,86,184,59,176,106,85,185,81,99,202,67,188,100,203,66,79,187,101,235,215,80,232,180,98,214,216,247,251,220,238,217,233,250,97,65,78,189,315,301,304,313 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 321 = 1 + 5*64, from a common submagma at infinity. C(E, M, k, B) adjoins a submagma M (m elements) of a model E to every group of a transversal design TD(k, g), g = |E| - m, so that every enlarged group is a copy of E and all of them share M; every block carries B, a model of order k in which x*x = x. Two elements of M multiply in M; an element of M or of group i with one of group i, in group i's copy of E; elements of different groups, in their block. It satisfies Equation 677 whenever E and B do. This magma is C(E, M, 5, B) with E = magma#8e5759f62ba231b7a190308c910bac46805bb85b5237b53b53611999ba1c2d7b, M = {60} in E, B = magma#e549b5f8492c9b6b5ad530e3aa4f39c6e23d08645ebd1b36a3c2de2a5a23bac5. Labels: 0..m-1 are M, in increasing order of their labels in E; m + g*i + c (i < k, c < g) is point c of group i, which plays the c-th element of E outside M, in increasing order. A block's point in group i plays element i of B. TD(5, 64): MacNeish's product over GF(64); GF(64) = F_2[x]/(x^6 + x + 1); GF(p^r) = F_p[x]/(f) labels c_0 + c_1 x + ... as c_0 + c_1 p + ..., and point c of a group is the c-th element of the product in lexicographic order. Block (a, b), a and b in the product, meets group i in the point whose coordinate in each field is a + s_i b, s_i the element of that field labelled i, or b when the field has exactly i elements. Equation 255: satisfied. Idempotent elements: 21.

last edited by qawbecrdtey at 2026-10-01 22:45:08 · history