Equation 677 Database

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Magma f476e2c2fe68…

magma f476e2c2fe68
Size
705
Isomorphism class hash
f476e2c2fe68e5f33d2ef3de42eb336a13bbff5d38a3a1abb859054eec0ec40b
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 20:39:48
Display reorder
660,450,304,474,122,510,305,451,475,120,511,452,303,121,476,512,300,449,473,118,509,301,447,471,119,507,302,448,472,117,508,441,295,465,128,501,442,296,466,126,502,443,294,467,127,503,298,444,468,124,504,299,445,469,125,505,297,446,470,123,506,679,681,684,687,196,269,114,95,351,267,197,115,93,352,195,268,94,116,353,265,199,113,98,350,266,200,111,96,348,264,198,112,97,349,194,275,105,101,342,192,273,106,99,343,193,274,107,100,344,271,190,108,104,345,272,191,109,102,346,270,189,110,103,347,661,667,662,664,363,27,285,423,549,28,364,286,424,550,365,29,425,287,551,26,362,284,422,548,24,360,282,420,546,25,361,283,421,547,354,33,276,414,540,355,34,277,415,541,356,35,278,416,542,32,357,279,417,543,30,358,280,418,544,31,359,281,419,545,676,673,688,678,640,237,639,638,636,238,648,647,646,645,656,239,654,655,653,236,632,631,630,628,234,616,615,614,612,235,624,623,622,620,80,228,290,215,73,78,229,288,213,74,79,230,289,214,72,231,589,588,593,592,232,600,599,598,597,233,608,607,606,605,697,698,703,704,313,133,375,435,561,134,314,376,436,562,312,132,437,377,563,129,316,374,434,560,130,317,372,432,558,131,315,373,433,559,311,139,366,426,552,309,140,367,427,553,310,138,368,428,554,135,307,369,429,555,136,308,370,430,556,137,306,371,431,557,689,690,694,691,381,218,44,399,207,216,382,42,400,208,383,217,401,43,209,221,380,47,398,210,219,378,45,396,211,220,379,46,397,212,387,224,39,390,205,388,222,40,391,206,389,223,41,392,204,227,386,38,393,201,225,384,36,394,202,226,385,37,395,203,672,666,670,663,583,175,582,142,0,176,585,584,143,2,587,174,141,586,1,171,580,581,145,4,172,577,576,146,5,173,579,578,144,3,565,166,564,148,7,566,167,567,149,8,569,165,568,147,6,169,570,571,151,10,170,572,573,152,11,168,574,575,150,9,696,695,693,692,486,62,522,534,462,60,487,523,535,463,488,61,536,524,464,65,485,521,533,461,63,483,519,531,459,64,484,520,532,460,477,68,513,525,453,478,66,514,526,454,479,67,515,527,455,71,480,516,528,456,69,481,517,529,457,70,482,518,530,458,682,685,680,686,643,56,637,642,641,54,651,644,650,649,659,55,658,652,657,59,635,629,634,633,57,619,613,618,617,58,627,621,626,625,537,51,77,438,291,538,52,75,439,292,539,53,76,440,293,50,595,594,591,590,48,603,596,602,601,49,611,604,610,609,702,701,699,700,411,188,261,243,90,186,412,262,244,91,413,187,245,263,92,184,410,260,242,89,185,408,258,240,87,183,409,259,241,88,402,179,252,249,81,403,177,253,250,82,404,178,254,251,83,182,405,255,248,84,180,406,256,246,85,181,407,257,247,86,665,668,669,671,14,163,318,498,339,164,12,319,499,340,13,162,500,320,341,159,17,321,497,338,160,15,322,495,336,161,16,323,496,337,20,154,324,489,330,18,155,325,490,331,19,153,326,491,332,157,23,327,492,333,158,21,328,493,334,156,22,329,494,335,674,677,675,683 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#c93f531644bb5fd38eabd6a6f62492ff6d9a38e5937df79a955f96fa67b29b12, 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 20:39:48 · history