Equation 677 Database

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Magma d2415fbd3be4…

magma d2415fbd3be4
Size
705
Isomorphism class hash
d2415fbd3be445e96a26a3b3991853753520359f0b99044c940341199a4c6614
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 20:40:37
Display reorder
660,267,550,23,452,438,265,548,21,450,436,266,549,22,451,437,455,553,263,19,441,20,264,551,453,439,552,262,454,440,18,545,14,273,447,433,546,12,271,448,434,13,547,272,449,435,269,17,544,446,432,15,542,270,444,430,543,16,268,445,431,679,677,674,685,390,476,72,303,290,388,474,73,301,291,389,475,74,302,289,299,479,393,75,286,76,391,477,300,287,478,392,298,288,77,471,78,385,309,296,472,79,386,307,297,80,473,387,308,295,384,81,470,305,292,82,468,382,306,293,469,83,383,304,294,670,671,664,668,414,500,126,564,162,412,498,124,562,160,413,499,125,563,161,567,503,417,129,165,127,415,501,565,163,502,416,566,164,128,495,132,409,559,157,496,130,410,560,158,131,497,411,561,159,408,135,494,558,156,133,492,406,556,154,493,134,407,557,155,687,678,676,681,632,634,116,628,629,616,618,117,613,612,624,626,115,620,621,652,658,656,112,653,113,640,642,637,636,650,648,645,644,114,594,122,592,589,588,602,123,600,597,596,121,610,608,604,605,581,118,583,585,584,119,528,152,87,85,529,120,153,86,84,703,699,704,700,60,54,28,339,329,61,55,29,337,330,62,56,27,338,328,335,57,63,24,332,25,64,58,336,333,59,65,334,331,26,52,34,66,345,327,53,35,67,343,325,33,51,68,344,326,69,30,48,341,323,31,49,70,342,324,50,32,71,340,322,691,693,690,689,174,464,104,402,139,172,462,105,400,140,173,463,103,401,141,405,467,177,100,138,101,175,465,403,136,466,176,404,137,102,459,110,169,397,145,460,111,170,398,146,109,461,171,399,147,168,106,458,396,144,107,456,166,394,142,457,108,167,395,143,665,661,662,667,211,240,183,237,224,212,238,181,235,225,213,239,182,236,223,233,243,210,179,220,180,208,241,234,221,242,209,232,222,178,246,189,202,228,215,244,187,203,226,216,188,245,204,227,214,205,185,249,231,218,186,247,206,229,219,248,184,207,230,217,695,694,696,692,250,538,190,512,576,251,536,191,510,574,252,537,192,511,575,515,541,253,193,579,194,254,539,513,577,540,255,514,578,195,533,196,256,507,571,534,197,257,508,572,198,535,258,509,573,259,199,532,506,570,200,530,260,504,568,531,201,261,505,569,682,688,680,684,630,635,41,633,631,614,619,39,617,615,622,627,40,625,623,657,659,654,37,655,38,638,643,641,639,651,646,649,647,36,595,47,590,593,591,603,45,598,601,599,46,611,606,609,607,586,43,587,582,580,44,554,148,442,150,555,42,149,443,151,697,698,701,702,313,488,274,426,366,314,486,275,424,364,315,487,276,425,365,429,491,312,277,369,278,310,489,427,367,490,311,428,368,279,483,280,319,421,361,484,281,320,422,362,282,485,321,423,363,318,283,482,420,360,284,480,316,418,358,481,285,317,419,359,666,663,672,669,6,524,91,354,378,7,522,92,352,376,8,523,93,353,377,357,527,9,90,381,88,10,525,355,379,526,11,356,380,89,519,97,4,349,373,520,98,5,350,374,99,521,3,351,375,1,96,518,348,372,94,516,0,346,370,517,95,2,347,371,673,675,686,683 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#cb0e3d6c08ee89c5c6b2b247efbea2db23079510829d72f3f07184542ed1a6a6, 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 20:40:38 · history