Equation 677 Database

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Magma 53c7316c1bea…

magma 53c7316c1bea
Size
705
Isomorphism class hash
53c7316c1bea26bb96e38901a47f68afbc7423231ef7a0be6adb3ce412063054
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 16:42:01
Display reorder
660,346,529,177,492,454,455,530,347,178,493,528,453,345,179,491,457,349,532,176,495,350,458,533,174,496,348,456,531,175,494,344,527,168,452,490,342,525,169,450,488,343,526,170,451,489,523,340,171,448,486,524,341,172,449,487,522,339,173,447,485,675,682,685,679,263,114,94,222,122,120,115,261,95,223,116,121,262,93,224,125,266,117,90,225,264,123,118,91,226,265,124,119,92,227,258,112,85,128,220,259,113,86,126,221,260,111,84,127,219,108,257,88,131,216,109,255,89,129,217,110,256,87,130,218,670,672,666,661,478,555,97,322,505,506,556,479,98,323,554,504,477,96,321,508,481,558,100,325,482,509,559,101,326,480,507,557,99,324,476,553,103,503,320,474,551,104,501,318,475,552,102,502,319,549,472,106,499,316,550,473,107,500,317,548,471,105,498,315,680,673,687,683,620,623,231,621,626,634,631,629,232,628,615,618,612,233,613,650,644,647,234,645,653,658,655,235,652,636,642,639,236,637,605,607,237,610,604,589,591,238,594,588,597,599,239,602,596,574,572,240,577,576,583,582,241,586,581,483,230,242,534,229,703,702,697,704,183,370,279,430,382,383,371,184,280,431,369,381,185,281,429,385,182,373,282,433,180,386,374,283,434,181,384,372,284,432,189,368,285,380,428,190,366,286,378,426,191,367,287,379,427,364,188,288,376,424,365,186,289,377,425,363,187,290,375,423,693,694,691,692,543,334,159,517,466,467,335,544,160,518,333,465,542,161,516,469,546,337,158,520,547,470,338,156,521,545,468,336,157,519,541,332,165,464,515,539,330,166,462,513,540,331,167,463,514,328,537,164,460,511,329,538,162,461,512,327,536,163,459,510,671,668,662,665,70,44,139,6,310,311,42,71,140,7,43,309,69,138,5,313,66,47,142,9,67,314,45,143,10,68,312,46,141,8,61,39,137,308,4,62,40,135,306,2,60,41,136,307,3,38,64,133,304,1,36,65,134,305,11,37,63,132,303,0,689,695,696,690,442,55,155,567,406,407,56,443,153,568,54,405,441,154,566,409,445,58,151,570,446,410,59,152,571,444,408,57,150,569,440,53,146,404,565,438,51,144,402,563,439,52,145,403,564,49,436,149,400,561,50,437,147,401,562,48,435,148,399,560,678,688,681,677,624,627,12,622,625,633,635,632,13,630,619,617,616,14,614,649,648,651,15,646,656,657,659,16,654,640,641,643,17,638,608,611,18,609,606,592,595,19,593,590,600,603,20,601,598,579,578,21,575,573,587,584,22,585,580,535,484,23,497,228,699,698,701,700,78,254,276,418,358,359,252,79,277,419,253,357,80,278,417,361,81,250,275,421,82,362,251,273,422,83,360,249,274,420,76,245,267,356,416,77,243,268,354,414,75,244,269,355,415,248,72,270,352,412,246,73,271,353,413,247,74,272,351,411,669,663,667,664,32,194,301,394,208,209,192,30,302,395,193,207,31,300,393,204,35,197,297,397,33,205,195,298,398,34,206,196,299,396,27,200,292,214,392,28,198,293,215,390,29,199,291,213,391,203,26,295,210,388,201,24,296,211,389,202,25,294,212,387,686,676,684,674 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#3a1e3dea02005faeb7a32ea89e0ebcd7060d0e295c5a20add7fb441719113d75, 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 16:42:02 · history