Equation 677 Database

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Magma 053c0d994380…

magma 053c0d994380
Size
705
Isomorphism class hash
053c0d9943806df2ceecc710c8c7240d6cc93d484002e77cf3cb6f4e3d6c81fe
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 15:10:19
Display reorder
660,505,370,282,346,455,283,506,347,456,371,284,369,504,345,454,508,281,373,349,458,509,279,374,350,459,507,280,372,348,457,288,368,344,503,453,289,366,342,501,451,290,367,343,502,452,364,287,340,499,449,365,285,341,500,450,498,363,286,339,448,680,684,682,679,188,492,115,224,196,113,186,222,197,493,114,491,187,223,195,184,111,495,220,199,185,112,496,221,200,183,110,494,219,198,121,490,230,194,202,119,488,228,192,203,120,489,229,193,201,486,117,226,190,205,487,118,227,191,206,189,485,116,225,204,668,670,661,672,322,131,32,555,234,33,323,556,235,132,34,133,321,554,236,325,35,130,558,233,326,36,128,559,231,324,37,129,557,232,30,122,553,320,240,31,123,551,318,241,29,124,552,319,242,125,26,549,316,239,126,27,550,317,237,315,127,28,548,238,674,677,678,687,627,622,91,624,621,89,635,632,629,630,90,614,619,616,612,651,87,646,648,645,659,88,654,656,653,643,86,638,640,636,97,606,608,611,605,95,590,592,595,588,96,598,600,603,597,572,93,574,577,576,582,94,584,587,580,535,447,92,472,1,704,702,703,699,48,418,292,406,430,293,49,407,431,419,291,417,47,405,429,44,295,421,409,433,45,296,422,410,434,46,294,420,408,432,298,416,404,39,428,299,414,402,40,426,297,415,403,38,427,412,301,400,42,424,413,302,401,43,425,41,411,300,399,423,692,689,693,691,358,442,135,334,543,136,359,335,544,443,134,441,357,333,542,361,138,445,337,546,362,139,446,338,547,360,137,444,336,545,141,440,332,356,541,142,438,330,354,539,140,439,331,355,540,436,144,328,352,537,437,145,329,353,538,351,435,143,327,536,666,664,671,662,310,215,173,152,58,174,311,153,56,213,175,214,309,154,57,313,172,218,155,61,314,170,216,156,59,312,171,217,157,60,179,210,150,308,53,180,211,151,306,54,181,212,149,307,55,209,178,146,304,52,207,176,147,305,50,303,208,177,148,51,695,690,696,694,567,530,15,250,262,16,568,251,263,531,14,529,566,249,261,570,18,533,253,265,571,19,534,254,266,569,17,532,252,264,21,528,248,565,260,22,526,246,563,258,20,527,247,564,259,524,24,244,561,256,525,25,245,562,257,560,523,23,243,255,686,688,675,673,625,620,7,626,623,5,633,634,631,628,6,613,617,618,615,649,3,644,650,647,657,4,652,658,655,641,2,637,642,639,13,604,610,609,607,11,589,594,593,591,12,596,602,601,599,578,9,579,575,573,581,10,586,585,583,497,182,8,510,0,698,700,697,701,480,518,68,394,109,69,481,395,107,519,70,517,479,393,108,483,71,521,397,105,484,72,522,398,106,482,73,520,396,104,66,516,392,478,100,67,514,390,476,98,65,515,391,477,99,512,62,388,474,103,513,63,389,475,101,473,511,64,387,102,669,667,663,665,161,467,85,382,267,83,162,383,268,468,84,466,163,381,269,160,81,470,385,270,158,82,471,386,271,159,80,469,384,272,76,465,380,167,273,74,463,378,168,274,75,464,379,169,275,461,79,376,166,276,462,77,377,164,277,165,460,78,375,278,683,685,676,681 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#06e28404eb43925716bfc8e4d73e8cc7ccb918742e903c176b52de636b48f456, 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 15:10:20 · history