Equation 677 Database

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Magma 7e506d71dd91…

magma 7e506d71dd91
Size
451
Isomorphism class hash
7e506d71dd918af897e60b1998ebb85a5f0b7580a820644fe198a76c9b9259ee
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
2026-10-07 07:30:52
Display reorder
446,441,440,442,447,443,448,449,445,444,450,146,103,324,196,312,176,288,164,339,82,147,96,325,197,313,177,289,165,340,83,148,97,326,198,314,178,290,166,341,84,98,149,327,191,307,179,283,159,342,85,150,99,328,192,308,180,284,160,343,86,87,100,143,329,193,309,181,285,161,344,80,101,144,330,194,310,182,286,162,345,81,102,145,323,195,311,175,287,163,351,2,1,14,28,10,11,8,22,379,378,380,381,377,374,375,376,373,372,389,388,390,391,387,384,385,386,383,382,399,398,400,401,397,394,395,396,393,392,408,409,410,411,407,404,405,406,403,402,419,418,420,421,417,414,415,416,413,412,422,428,429,430,431,427,424,425,426,423,352,358,359,360,361,357,354,355,356,353,362,368,369,370,371,367,364,365,366,363,434,439,435,437,438,432,433,436,248,139,282,116,306,76,263,230,208,50,249,140,275,117,299,77,264,231,209,51,250,141,276,118,300,78,265,232,210,52,142,251,277,119,301,79,266,233,211,53,244,135,278,112,302,72,260,234,212,54,55,136,245,279,113,303,73,261,235,213,48,137,246,280,114,304,74,262,229,214,49,138,247,281,115,305,75,350,349,207,12,13,16,30,18,24,29,20,33,335,95,127,316,41,186,228,169,154,32,336,88,128,317,42,187,222,170,155,34,337,89,129,318,43,188,223,171,156,338,35,90,130,319,44,189,224,172,157,36,331,91,131,320,45,190,225,173,158,151,332,37,92,132,321,46,183,226,174,152,333,38,93,133,322,47,184,227,167,153,334,39,94,134,315,40,185,348,168,3,4,5,7,15,21,26,6,68,111,62,257,267,243,126,199,218,291,69,104,63,258,268,236,122,200,219,292,70,105,56,259,269,237,123,201,220,293,106,71,57,252,270,238,124,202,221,294,64,107,58,253,271,239,125,203,215,295,296,108,65,59,254,272,240,120,204,216,297,109,66,60,255,273,241,121,205,217,298,110,67,61,256,274,242,346,206,347,9,0,17,31,19,23,27,25 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#3ec10e0f3130094455629e6582ff2efb75d44ca91c712c76da4b28ee38e971b6, 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 2026-10-07 07:30:53 · history