Equation 677 Database

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Magma 504588458522…

magma 504588458522
Size
705
Isomorphism class hash
504588458522206310192a523725ca96fa2d013831fe0d047d13f570c24a3013
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 704) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-03 15:13:52
Display reorder
660,503,281,394,339,466,504,282,395,340,467,502,283,393,341,465,506,280,397,342,469,278,507,398,343,470,279,505,396,344,468,501,287,392,345,464,499,288,390,346,462,500,289,391,347,463,286,497,388,348,460,284,498,389,349,461,285,496,387,350,459,674,680,682,676,479,76,101,116,32,480,77,102,117,30,478,78,100,115,31,482,79,104,112,28,80,483,105,113,29,81,481,103,114,27,477,82,107,122,38,475,83,108,123,36,476,84,106,121,37,85,473,110,118,34,86,474,111,119,35,87,472,109,120,33,668,663,666,672,491,254,527,430,418,492,255,528,431,419,490,256,526,429,417,494,257,530,433,421,258,495,531,434,422,259,493,529,432,420,489,260,525,428,416,487,261,523,426,414,488,262,524,427,415,263,485,521,424,412,264,486,522,425,413,265,484,520,423,411,678,677,681,685,621,54,620,626,622,629,55,628,634,630,612,56,613,618,614,644,53,645,650,646,51,653,652,658,654,52,636,637,642,638,605,60,604,610,606,588,61,589,594,590,596,62,597,602,598,59,572,573,577,576,57,581,580,586,582,58,25,24,544,26,702,698,704,703,307,197,358,370,300,305,198,359,371,301,306,199,357,369,299,303,196,361,373,296,194,304,362,374,297,195,302,360,372,298,313,203,356,368,291,311,204,354,366,292,312,205,355,367,290,202,309,352,364,294,200,310,353,365,295,201,308,351,363,293,691,692,694,690,515,15,229,240,334,516,16,227,241,335,514,17,228,239,333,518,14,225,236,337,12,519,226,237,338,13,517,224,238,336,513,21,220,231,332,511,22,218,232,330,512,23,219,230,331,20,509,223,234,328,18,510,221,235,329,19,508,222,233,327,661,662,669,670,145,324,157,169,175,146,325,158,170,173,147,323,159,168,174,144,320,156,160,171,321,142,154,571,570,322,143,155,167,172,136,315,148,163,181,137,316,149,161,179,138,314,150,162,180,318,139,151,166,177,319,140,152,164,178,317,141,153,165,176,695,696,689,693,442,269,565,539,66,443,270,566,540,67,441,271,564,538,68,445,268,568,542,65,266,446,569,543,63,267,444,567,541,64,440,275,563,537,72,438,276,561,535,73,439,277,562,536,74,274,436,559,533,71,272,437,560,534,69,273,435,558,532,70,686,683,679,687,624,183,627,625,623,632,184,635,633,631,616,182,619,617,615,648,186,651,649,647,187,656,659,657,655,185,640,643,641,639,608,189,611,609,607,592,190,595,593,591,600,188,603,601,599,192,578,579,575,574,193,584,587,585,583,191,326,545,471,75,700,701,697,699,553,42,91,454,406,554,43,92,455,407,552,44,93,453,405,556,41,90,457,409,39,557,88,458,410,40,555,89,456,408,551,48,97,452,404,549,49,98,450,402,550,50,99,451,403,47,547,96,448,400,45,548,94,449,401,46,546,95,447,399,665,664,671,667,4,209,249,382,130,5,210,250,383,131,3,211,248,381,132,1,208,252,385,133,206,0,253,386,134,207,2,251,384,135,10,215,247,380,128,11,216,245,378,129,9,217,246,379,127,214,6,243,376,124,212,7,244,377,125,213,8,242,375,126,675,684,688,673 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 705 = 1 + 11*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, 11, B) with E = magma#0c204955552ad126415d2d3170da1bc3e83549814dfd47378340ca39d32aede4, M = {60} in E, B = magma#abfd8e025ce71b705594dbbe1465dc1c7328d12d30e12d07906d7138f9d583bc. 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(11, 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: 45.

last edited by qawbecrdtey at 2026-10-03 15:13:54 · history