Equation 677 Database

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Magma 781c8193e0f5…

magma 781c8193e0f5
Size
595
Isomorphism class hash
781c8193e0f5373f8867bc81bde9b5fb5f0b3eed3efd50ca03c05f234bbbbcbc
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
2026-10-08 21:25:53
Display reorder
41,77,49,22,65,39,78,50,23,66,40,76,51,21,67,46,25,38,80,62,47,26,36,81,63,48,24,37,79,64,512,521,510,511,514,509,505,508,504,503,506,507,487,486,478,479,488,461,468,218,270,268,243,269,240,223,187,191,190,189,183,184,150,293,300,318,315,301,317,298,372,408,414,412,410,406,407,378,368,390,382,409,413,411,313,309,310,314,319,302,316,141,160,137,151,142,158,188,112,110,108,95,94,114,115,166,192,161,136,152,157,140,106,111,109,107,97,96,113,283,277,284,276,271,273,278,168,117,167,116,169,571,570,589,590,592,593,587,588,591,543,528,516,542,529,524,523,59,75,87,58,31,85,93,60,92,105,104,27,10,9,474,466,457,471,473,465,458,472,477,467,476,485,484,456,255,208,236,226,248,252,234,146,171,181,156,178,185,186,448,452,447,449,451,453,450,307,312,311,294,296,303,304,144,130,177,131,145,155,170,280,275,279,281,282,272,274,247,251,209,254,210,235,228,250,261,237,257,267,266,225,380,392,395,356,400,357,389,387,329,386,328,388,578,579,550,551,530,532,527,533,541,580,586,583,584,581,585,582,489,499,498,494,492,501,495,475,459,480,482,462,464,455,212,202,232,246,244,227,213,84,32,89,42,98,101,57,14,5,4,52,74,71,30,214,249,229,256,230,264,265,497,491,490,493,500,496,502,460,481,483,463,454,470,469,16,6,12,55,17,28,82,33,90,43,99,103,53,3,73,72,7,13,56,29,18,83,34,91,44,100,102,54,324,332,331,325,326,327,330,69,165,242,164,70,577,576,568,522,539,526,525,538,569,519,513,574,549,575,520,548,86,35,88,0,1,45,20,221,220,200,199,197,241,217,179,173,123,147,174,118,120,149,143,139,138,126,125,159,180,135,172,124,148,175,119,193,231,224,222,219,201,198,383,401,365,333,376,373,370,431,423,422,420,441,434,442,335,367,403,385,336,334,377,374,371,369,347,346,345,393,295,305,292,308,299,285,286,435,433,432,430,424,421,419,394,375,396,366,402,384,416,321,417,415,418,320,537,540,534,559,531,558,552,560,557,546,556,547,544,555,545,594,61,8,19,11,2,15,68,233,204,206,263,260,194,196,397,381,404,354,363,360,351,361,391,379,352,355,405,342,253,195,239,259,245,215,211,127,133,162,153,128,129,182,121,176,122,132,134,163,154,203,207,262,258,238,205,216,348,344,398,340,349,358,362,440,436,425,427,445,444,438,353,364,343,399,341,359,350,429,439,437,426,428,446,443,297,290,291,289,306,288,287,338,323,337,322,339,554,553,562,564,561,565,566,563,567,517,515,573,535,572,518,536 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#a8026a02368cc98eace7a76910bb242dec082e21ec6371f1fc7226b87fb07666, M = the submagma generated by {2, 4} (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 2026-10-08 21:25:54 · history