Equation 677 Database

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Magma 54d8c36bd94f…

magma 54d8c36bd94f
Size
595
Isomorphism class hash
54d8c36bd94f779da5dafaf52bd738c8aaac926eef045c6c1516ed2b975c1ec1
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 594) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-07 03:27:01
Display reorder
278,277,279,280,281,276,393,395,394,396,397,398,402,404,403,400,401,399,408,421,409,407,405,406,431,430,432,428,427,429,524,525,526,523,582,272,271,274,275,270,273,296,295,297,298,299,294,257,256,252,253,254,255,80,79,81,82,83,78,67,66,68,69,70,71,250,249,251,246,247,248,136,135,137,132,133,134,306,311,307,308,309,310,17,16,12,13,14,15,317,316,312,313,314,315,75,74,76,77,72,73,435,433,434,436,437,438,336,338,337,340,341,339,354,353,352,357,355,356,440,500,501,509,502,503,418,483,457,482,459,481,532,528,538,527,518,588,552,544,585,551,559,590,581,548,591,577,130,129,126,127,128,131,321,320,322,323,318,319,262,261,263,258,259,260,53,52,48,49,50,51,203,202,198,199,200,201,64,63,65,60,61,62,3,2,4,5,1,0,300,305,301,302,303,304,265,264,266,267,268,269,58,57,59,54,55,56,241,240,242,243,244,245,495,494,496,471,470,493,486,485,506,466,467,424,461,460,462,474,472,473,343,345,344,342,420,419,425,489,469,488,468,487,512,531,511,516,521,592,553,587,557,549,580,589,550,576,543,578,30,35,32,33,34,31,221,220,216,217,218,219,191,190,186,187,188,189,167,166,162,163,164,165,184,183,185,180,181,182,92,91,93,94,95,90,125,124,120,121,122,123,325,324,326,327,328,329,116,115,117,118,119,114,234,239,235,236,237,238,293,292,288,289,290,291,411,410,412,415,413,414,369,368,367,370,371,372,373,375,374,376,377,378,490,492,491,441,507,426,497,439,498,508,499,442,537,529,536,522,520,571,562,561,586,563,579,593,573,584,575,565,210,215,212,213,214,211,8,7,9,10,11,6,110,109,111,112,113,108,285,284,286,287,282,283,139,138,140,141,142,143,173,172,168,169,170,171,154,153,155,150,151,152,230,229,231,232,233,228,227,226,222,223,224,225,37,36,38,39,40,41,196,195,197,192,193,194,346,348,347,350,351,349,389,388,390,392,391,448,455,456,416,480,417,454,359,358,360,363,361,362,366,365,505,478,504,364,514,533,510,519,515,566,583,554,564,556,572,574,570,567,540,569,44,43,46,47,42,45,146,145,147,148,149,144,158,157,159,160,161,156,335,334,330,331,332,333,106,105,107,102,103,104,178,177,179,174,175,176,101,100,96,97,98,99,88,87,89,84,85,86,21,20,22,23,18,19,209,208,204,205,206,207,26,25,27,28,29,24,484,464,463,422,423,465,452,451,453,458,449,450,446,447,387,479,386,445,379,380,384,382,385,381,383,475,443,477,444,476,534,530,513,517,535,555,594,547,560,546,539,545,541,542,568,558 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 595 = 35 + 5*112, 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#83fb73755ed07f789756511d0e776415c2bd28bb0aaa387c6c265081499d5ced, M = the submagma generated by {24, 72} (35 elements) 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, 112): MacNeish's product over GF(16) x GF(7); GF(16) = F_2[x]/(x^4 + 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: 85.

last edited by qawbecrdtey at 2026-10-07 03:27:02 · history