Equation 677 Database

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Magma 7f3b421686e6…

magma 7f3b421686e6
Size
451
Isomorphism class hash
7f3b421686e6c6b307811b612d19f3bd57478bba0d5e21bcfb1e59785b9b333f
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 450) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-08 13:09:57
Display reorder
448,440,444,445,446,447,449,442,441,443,450,203,311,128,59,117,71,44,325,339,216,196,312,129,60,110,72,37,326,340,217,313,197,130,61,111,73,38,327,341,218,314,198,131,54,112,74,39,328,342,219,307,199,132,55,113,75,40,329,343,212,213,200,308,125,56,114,76,41,330,344,201,214,309,126,57,115,77,42,323,345,202,215,310,127,58,116,70,43,324,351,5,1,14,28,10,11,4,22,375,376,373,372,374,380,381,377,378,379,385,386,383,382,384,390,391,387,388,389,396,395,393,392,394,400,401,397,398,399,406,405,403,402,404,410,411,407,408,409,416,415,413,412,414,420,421,417,418,419,429,425,426,423,422,424,430,431,427,428,355,359,356,353,352,354,360,361,357,358,365,369,366,363,362,364,370,371,367,368,434,439,435,437,438,432,433,436,252,141,161,286,97,176,234,103,272,306,253,142,162,287,98,177,228,104,273,299,143,254,163,288,99,178,229,105,274,300,144,255,156,289,100,179,230,106,267,301,145,256,157,290,102,172,231,107,268,302,303,257,146,158,283,101,173,232,108,269,258,304,147,159,284,95,174,233,109,270,251,305,148,160,285,96,175,350,347,271,12,13,16,30,18,24,29,20,250,335,48,316,210,224,193,123,64,136,243,336,49,317,211,225,194,124,65,137,337,244,50,318,204,226,195,118,66,138,338,245,51,319,205,227,188,119,67,139,331,246,52,320,206,220,189,120,68,140,133,247,332,53,321,207,221,190,121,69,248,134,333,46,322,208,222,191,122,62,249,135,334,47,315,209,223,192,348,63,6,7,8,3,15,21,26,2,265,180,83,291,238,280,152,92,45,169,266,181,84,292,239,281,153,94,33,170,182,259,85,293,240,282,154,86,93,171,183,260,78,294,241,275,155,87,34,164,184,261,79,295,242,276,149,88,35,165,166,262,185,80,296,235,277,150,89,36,263,167,186,81,297,236,278,151,90,32,264,168,187,82,298,237,279,349,91,346,9,0,17,31,19,23,27,25 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 451 = 11 + 5*88, 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#ceaa5cf66e9e90f9a18f98abca872d4f40876d9d61f36b41c766b39b4449cf81, M = {88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98} 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, 88): MacNeish's product over GF(8) x GF(11); GF(8) = F_2[x]/(x^3 + 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: 11.

last edited by qawbecrdtey at 2026-10-08 13:09:59 · history