Equation 677 Database

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Magma 572e840ed3c6…

magma 572e840ed3c6
Size
705
Isomorphism class hash
572e840ed3c679416b03ef64cbff40721580123a10807e5660fdcdff53527c8a
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 16:29:50
Display reorder
660,539,275,405,379,14,537,276,13,403,377,538,277,18,404,378,535,274,15,401,375,536,272,16,402,376,534,273,17,400,374,545,266,25,411,385,267,27,409,543,383,268,30,410,544,384,24,269,407,541,381,19,270,408,542,382,22,271,406,540,380,686,681,676,677,515,150,202,453,429,513,151,427,200,451,514,149,428,201,452,511,146,425,205,449,512,147,426,203,450,510,148,424,204,448,521,156,435,197,459,157,433,198,519,457,155,434,199,520,458,431,152,196,517,455,432,153,194,518,456,430,154,195,516,454,662,667,663,669,503,84,417,169,170,501,82,171,415,167,502,83,172,416,168,499,80,173,413,165,500,81,174,414,166,498,79,175,412,164,509,90,176,423,160,88,177,421,507,158,89,178,422,508,159,179,86,419,505,163,180,87,420,506,161,181,85,418,504,162,674,680,682,678,398,10,391,23,496,396,11,494,389,20,397,12,495,390,21,394,9,492,387,29,395,7,493,388,26,393,8,491,386,28,654,0,657,656,653,2,641,640,638,637,3,649,648,646,645,622,4,621,625,624,633,5,632,630,628,497,6,392,399,1,704,699,703,700,250,282,527,441,465,248,283,463,525,439,249,281,464,526,440,253,278,461,523,437,251,279,462,524,438,252,280,460,522,436,245,288,471,533,447,289,469,531,246,445,287,470,532,247,446,467,284,529,244,443,468,285,530,242,444,466,286,528,243,442,692,689,691,693,52,37,484,363,575,53,38,573,482,364,54,39,574,483,362,51,40,571,480,366,49,41,572,481,367,50,42,570,479,365,43,35,581,490,369,36,579,488,44,370,34,580,489,45,368,577,31,486,46,372,578,32,487,47,373,576,33,485,48,371,671,664,668,665,355,73,341,127,308,353,74,309,342,125,354,75,310,343,126,351,76,311,340,123,352,77,312,338,124,350,78,313,339,122,361,71,306,347,133,72,307,348,359,131,70,305,349,360,132,302,67,346,357,129,303,68,344,358,130,304,69,345,356,128,695,690,696,694,613,187,331,319,594,611,185,592,329,317,612,186,593,330,318,609,183,590,327,315,610,184,591,328,316,608,182,589,326,314,619,193,600,337,325,191,598,335,617,323,192,599,336,618,324,596,189,333,615,321,597,190,334,616,322,595,188,332,614,320,685,688,673,675,587,136,606,474,108,585,134,109,604,472,586,135,107,605,473,583,139,104,602,477,584,137,105,603,475,582,138,106,601,476,658,142,652,659,655,140,636,643,642,639,141,644,651,650,647,626,145,627,623,620,629,143,635,634,631,103,144,607,588,478,698,701,697,702,551,92,241,216,228,549,93,229,239,217,550,91,227,240,215,547,95,224,237,212,548,96,225,238,213,546,94,226,236,214,557,98,219,232,207,99,220,230,555,208,97,218,231,556,206,222,101,235,553,210,223,102,233,554,211,221,100,234,552,209,666,670,672,661,115,298,563,59,261,113,296,262,561,60,114,297,260,562,58,111,301,264,559,55,112,299,265,560,56,110,300,263,558,57,121,293,259,569,65,294,257,567,119,66,295,258,568,120,64,255,292,565,117,61,256,290,566,118,62,254,291,564,116,63,684,679,687,683 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#33fc7ab4b4817466950310b35dd4cd44cb4b00aed5b55945bbae0672c2180aa2, 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 16:29:51 · history