Equation 677 Database

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Magma 94d72884f1d1…

magma 94d72884f1d1
Size
705
Isomorphism class hash
94d72884f1d17b5a538649e1f7182cc2f3f5bd3a6efd028474bf1ae489977fc3
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 18:10:02
Display reorder
660,548,69,340,510,364,546,70,338,508,362,547,68,339,509,363,551,72,513,367,343,549,73,341,511,365,550,71,342,512,366,335,543,505,67,359,336,544,506,65,360,337,545,507,66,361,542,334,504,63,358,540,332,502,64,356,62,541,333,503,357,683,675,687,673,388,293,95,83,184,386,294,96,84,182,387,295,97,85,183,391,292,82,187,94,389,290,92,80,185,390,291,93,81,186,86,383,74,284,190,87,384,75,285,188,88,385,76,286,189,382,89,77,287,193,380,90,78,288,191,289,381,91,79,192,663,672,666,671,412,296,204,438,524,410,297,205,436,522,411,298,203,437,523,415,299,441,527,200,413,300,201,439,525,414,301,202,440,526,195,407,433,302,519,196,408,434,303,520,194,409,435,304,521,406,198,432,305,518,404,199,430,306,516,307,405,197,431,517,679,685,677,674,630,262,631,629,635,614,260,615,613,619,622,261,623,621,627,654,265,653,659,655,638,263,639,637,643,646,264,647,645,651,591,590,588,268,595,599,598,596,266,603,607,606,604,267,611,580,582,581,271,584,256,259,231,269,578,270,257,258,230,579,697,699,702,700,31,15,149,145,129,29,16,150,143,130,30,18,151,144,128,27,21,141,132,148,28,22,146,142,133,26,24,147,140,131,155,37,136,11,127,156,35,134,12,125,157,36,135,9,126,33,154,139,2,123,34,152,137,4,124,6,32,153,138,122,692,696,690,689,376,227,498,316,249,374,228,496,314,247,375,229,497,315,248,379,226,319,245,501,377,224,499,317,246,378,225,500,318,244,493,371,311,218,255,494,372,312,219,253,495,373,313,220,254,370,492,310,221,251,368,490,308,222,252,223,369,491,309,250,662,661,665,668,7,162,562,474,486,3,163,560,472,484,5,161,561,473,485,13,158,477,489,565,8,159,563,475,487,10,160,564,476,488,557,19,469,168,481,558,14,470,169,482,559,17,471,167,483,25,556,468,164,480,20,554,466,165,478,166,23,555,467,479,693,694,691,695,536,210,400,424,450,534,211,398,422,448,535,209,399,423,449,539,206,427,453,403,537,207,401,425,451,538,208,402,426,452,395,531,419,216,445,396,532,420,217,446,397,533,421,215,447,530,394,418,212,444,528,392,416,213,442,214,529,393,417,443,678,680,686,676,632,176,628,633,634,616,177,612,617,618,624,178,620,625,626,656,179,657,658,652,640,180,636,641,642,648,181,644,649,650,589,592,593,174,594,597,600,601,175,602,605,608,609,173,610,586,585,587,170,583,428,1,514,171,552,172,429,0,515,553,701,704,698,703,100,278,240,352,111,98,279,238,350,112,99,280,239,351,110,103,281,355,114,243,101,282,241,353,115,102,283,242,354,113,235,106,347,276,117,236,104,348,277,118,237,105,349,275,116,109,234,346,272,120,107,232,344,273,121,274,108,233,345,119,664,670,669,667,462,325,574,59,48,460,323,572,60,49,461,324,573,61,47,465,321,58,44,577,463,322,575,56,45,464,320,576,57,46,569,457,50,331,39,570,458,51,329,40,571,459,52,330,38,456,568,53,327,42,454,566,54,328,43,326,455,567,55,41,682,684,681,688 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#676093fc8b0a9c703c9b4a913f63a03a075a7ec27635c2c42c5b015ba025ae64, 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 18:10:03 · history