Equation 677 Database

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Magma 75845b525456…

magma 75845b525456
Size
705
Isomorphism class hash
75845b52545639ee06d19f44154eb960a07684c79dc7b7c96622d81db18566e4
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 16:52:46
Display reorder
660,164,573,489,465,522,162,466,574,490,523,163,467,575,491,524,167,572,464,488,521,165,570,462,486,519,166,571,463,487,520,480,564,159,456,513,481,565,160,457,514,482,566,161,458,515,567,483,158,459,516,568,484,156,460,517,569,485,157,461,518,681,679,683,687,56,441,369,534,393,54,535,442,370,394,55,536,443,371,395,59,440,533,368,392,57,438,531,366,390,58,439,532,367,391,360,432,51,525,384,361,433,52,526,385,362,434,53,527,386,435,363,50,528,387,436,364,48,529,388,437,365,49,530,389,662,666,663,665,42,293,281,303,561,43,304,291,279,562,44,305,292,280,563,45,289,302,277,560,46,290,300,278,558,47,288,301,276,559,272,284,40,294,552,270,282,41,295,553,271,283,39,296,554,287,275,36,297,555,285,273,37,298,556,286,274,38,299,557,673,675,685,674,70,642,637,638,640,71,646,650,645,648,69,654,658,652,656,66,634,630,628,632,67,618,614,613,616,68,626,622,620,624,346,510,61,265,492,347,511,62,266,493,345,512,60,264,494,591,589,64,592,593,602,599,65,596,600,610,607,63,604,608,703,697,700,704,18,175,126,400,417,19,401,176,127,418,20,399,174,128,419,21,178,396,129,416,22,179,397,130,414,23,177,398,131,415,124,173,16,406,408,125,171,17,407,409,123,172,15,405,410,169,120,12,402,411,170,121,13,403,412,168,122,14,404,413,693,689,690,692,77,240,229,255,217,75,256,241,230,218,76,257,242,228,216,73,243,254,232,220,74,244,252,233,221,72,245,253,231,219,235,246,83,261,223,236,247,81,262,224,234,248,82,263,222,249,238,79,260,226,250,239,80,258,227,251,237,78,259,225,671,661,668,670,201,328,507,107,33,202,105,329,508,34,203,106,327,509,35,200,324,103,506,32,198,325,104,504,30,199,326,102,505,31,498,319,192,98,24,499,320,193,96,25,500,318,194,97,26,322,501,195,101,27,323,502,196,99,28,321,503,197,100,29,694,695,696,691,209,453,477,585,315,207,586,454,478,316,208,587,455,479,317,205,452,584,476,314,206,450,582,474,312,204,451,583,475,313,468,444,215,576,306,469,445,213,577,307,470,446,214,578,308,447,471,211,579,309,448,472,212,580,310,449,473,210,581,311,680,688,676,678,340,636,643,641,639,341,649,644,651,647,339,657,653,659,655,336,629,633,635,631,337,612,617,619,615,338,621,625,627,623,549,268,331,495,344,550,269,332,496,342,551,267,330,497,343,594,595,334,590,588,597,603,335,601,598,605,611,333,609,606,702,701,698,699,84,350,429,109,6,85,110,348,430,7,86,108,349,431,8,87,353,112,428,9,88,351,113,426,10,89,352,111,427,11,420,356,90,115,4,421,354,91,116,5,422,355,92,114,3,359,423,93,118,1,357,424,94,119,0,358,425,95,117,2,664,672,667,669,188,146,133,546,381,186,547,144,134,382,187,548,145,132,383,191,149,545,136,380,189,147,543,137,378,190,148,544,135,379,139,152,183,537,372,140,150,184,538,373,138,151,185,539,374,155,142,182,540,375,153,143,180,541,376,154,141,181,542,377,686,684,677,682 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#458b3cfe489c9903ffdf95802569f7fced83cfa9f913419e94bc2fd3ec4c05bf, 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 16:52:47 · history