Equation 677 Database

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Magma 2b987af06528…

magma 2b987af06528
Size
705
Isomorphism class hash
2b987af0652827c2cc39286ec77efb407994a58e3882884241e4f9e30c913c1d
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 20:37:27
Display reorder
660,474,43,460,436,351,458,41,434,349,472,473,42,459,435,350,39,477,463,439,347,40,475,461,437,348,38,476,462,438,346,469,49,455,431,342,432,470,47,456,340,471,48,457,433,341,45,468,454,430,345,46,466,452,428,343,44,467,453,429,344,683,684,675,681,222,14,97,275,376,95,15,276,374,223,221,16,96,274,375,17,218,93,278,379,18,219,94,279,377,19,220,92,277,378,228,20,88,273,371,271,229,21,86,372,227,22,87,272,373,23,224,91,269,370,24,225,89,270,368,25,226,90,268,369,669,668,665,670,400,99,191,238,412,192,100,236,410,398,399,98,193,237,411,102,403,190,241,415,103,401,188,239,413,101,402,189,240,414,395,105,182,233,407,234,396,106,183,408,397,104,184,235,409,108,394,185,232,406,109,392,186,230,404,107,393,187,231,405,680,677,678,687,634,174,629,631,628,613,175,615,612,618,626,173,621,623,620,170,658,653,655,652,171,642,637,639,636,172,650,645,647,644,594,180,588,591,589,599,602,181,596,597,610,179,604,607,605,176,583,581,585,584,177,492,255,366,12,178,493,254,367,13,701,700,704,703,526,7,360,538,514,358,8,536,512,524,525,6,359,537,513,10,529,363,541,517,11,527,361,539,515,9,528,362,540,516,521,5,355,533,509,534,522,3,356,510,523,4,357,535,511,0,520,354,532,508,2,518,352,530,506,1,519,353,531,507,690,693,692,694,249,53,336,448,202,334,54,446,200,250,248,55,335,447,201,52,252,339,451,205,50,253,337,449,203,51,251,338,450,204,247,59,331,443,197,444,245,60,332,198,246,61,333,445,199,58,243,330,442,196,56,244,328,440,194,57,242,329,441,195,663,664,661,667,572,150,573,326,124,569,151,327,122,568,570,149,571,325,123,146,578,579,322,127,147,574,575,323,125,148,576,577,324,126,563,156,562,317,130,318,565,157,564,128,567,155,566,316,129,152,561,560,320,133,153,557,556,321,131,154,559,558,319,132,695,696,689,691,163,112,424,488,32,422,110,486,33,161,162,111,423,487,34,115,159,427,491,35,113,160,425,489,36,114,158,426,490,37,169,118,419,483,30,484,167,116,420,31,168,117,421,485,29,121,165,418,482,26,119,166,416,480,27,120,164,417,481,28,679,674,676,686,635,78,632,633,630,616,79,617,614,619,627,77,624,625,622,74,659,656,657,654,75,643,640,641,638,76,651,648,649,646,595,84,592,593,590,601,603,85,600,598,611,83,608,609,606,80,587,586,582,580,81,554,465,478,364,82,555,464,479,365,697,702,698,699,502,214,264,388,63,262,212,386,64,500,501,213,263,387,62,217,505,267,391,66,215,503,265,389,67,216,504,266,390,65,497,209,259,383,69,384,498,210,260,70,499,211,261,385,68,208,496,258,382,72,206,494,256,380,73,207,495,257,381,71,662,671,672,666,293,145,304,282,550,305,143,280,548,294,292,144,306,281,549,141,296,307,285,553,142,297,308,283,551,140,295,309,284,552,299,136,310,288,545,286,300,134,311,546,298,135,312,287,547,139,302,313,291,544,137,303,314,289,542,138,301,315,290,543,682,685,688,673 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#c6bb22b65ea8da42821d53c407d340f5ca33ab54805c0683c0d4385c20756f88, 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 20:37:28 · history