Equation 677 Database

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Magma 94eb179e6ac4…

magma 94eb179e6ac4
Size
705
Isomorphism class hash
94eb179e6ac4ee94048a223e5bcec26b6b573945ac46390119518b1f7f6d6132
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 18:23:17
Display reorder
660,163,556,514,580,5,557,581,164,515,3,555,579,162,513,4,552,166,510,576,0,553,167,511,577,2,554,165,512,578,1,161,520,562,586,11,159,521,563,587,9,160,519,561,585,10,516,157,558,582,7,517,158,559,583,8,518,156,560,584,6,674,686,685,683,56,108,223,370,315,109,371,54,224,316,110,369,55,222,317,111,59,226,366,314,112,57,227,367,312,113,58,225,368,313,51,221,114,376,321,52,219,115,377,322,53,220,116,375,323,217,50,117,372,320,218,48,118,373,318,216,49,119,374,319,669,662,661,663,127,424,382,358,490,425,359,128,383,491,423,357,126,381,489,420,130,378,354,486,421,131,379,355,487,422,129,380,356,488,125,388,430,364,496,123,389,431,365,497,124,387,429,363,495,384,121,426,360,492,385,122,427,361,493,386,120,428,362,494,681,675,679,676,35,336,592,483,526,337,484,33,593,527,338,485,34,591,525,339,31,588,482,522,340,32,589,480,523,341,30,590,481,524,26,650,646,648,649,24,658,654,656,657,25,642,638,640,641,615,29,614,616,617,626,27,622,624,625,634,28,630,632,633,704,700,703,701,168,244,502,103,460,245,104,169,503,461,243,102,170,501,459,240,171,498,106,456,241,172,499,107,457,242,173,500,105,458,174,508,250,101,466,175,509,251,99,467,176,507,249,100,465,504,177,246,97,462,505,178,247,98,463,506,179,248,96,464,690,694,693,691,153,472,448,335,14,473,333,154,449,12,471,334,155,447,13,468,152,444,331,17,469,150,445,332,15,470,151,446,330,16,144,454,478,326,20,145,455,479,324,18,146,453,477,325,19,450,147,474,329,23,451,148,475,327,21,452,149,476,328,22,672,667,666,665,95,279,293,193,270,280,194,93,291,271,281,192,94,292,272,278,91,289,196,273,276,92,290,197,274,277,90,288,195,275,86,299,285,199,268,84,297,286,200,269,85,298,287,198,267,295,89,284,202,264,296,87,282,203,265,294,88,283,201,266,695,689,696,692,143,304,394,604,412,305,605,141,395,413,303,603,142,393,411,300,139,390,600,408,301,140,391,601,409,302,138,392,602,410,134,400,310,610,418,132,401,311,611,419,133,399,309,609,417,396,137,306,606,414,397,135,307,607,415,398,136,308,608,416,678,688,673,677,40,598,405,208,212,599,209,41,406,210,597,207,39,407,211,594,36,404,204,215,595,37,402,205,213,596,38,403,206,214,46,647,651,645,644,47,655,659,653,652,45,639,643,636,637,618,42,619,612,613,623,43,627,621,620,631,44,635,629,628,699,698,702,697,234,544,436,568,350,545,569,235,437,348,543,567,236,435,349,540,237,432,564,353,541,238,433,565,351,542,239,434,566,352,232,442,550,574,345,233,443,551,575,346,231,441,549,573,347,438,228,546,570,344,439,229,547,571,342,440,230,548,572,343,671,670,668,664,65,532,256,191,83,533,189,63,257,81,531,190,64,255,82,528,61,252,187,79,529,62,253,188,80,530,60,254,186,78,71,262,538,182,74,69,263,539,180,72,70,261,537,181,73,258,67,534,185,77,259,68,535,183,75,260,66,536,184,76,680,687,684,682 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#7eb365a46a73bc671c535e7eab37a7fd590c6d5c6b4c14d45f700003c9150a2d, 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 18:23:18 · history