Equation 677 Database

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Magma 95448d2ee507…

magma 95448d2ee507
Size
705
Isomorphism class hash
95448d2ee5070ce31ba39e15c5490f2abdd44116cc21131f7879f6f50719da68
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 20:32:18
Display reorder
704,207,402,418,428,208,403,419,426,209,404,417,427,206,405,414,431,204,406,415,429,205,407,416,430,213,400,409,423,214,401,410,424,215,399,408,425,396,212,412,422,397,210,413,420,211,398,411,421,438,439,440,441,442,443,436,437,434,432,433,435,674,673,675,672,5,582,597,555,3,583,598,556,4,584,599,557,0,585,596,554,2,586,594,552,1,587,595,553,11,580,588,561,9,581,589,562,10,579,590,563,576,7,591,560,577,8,592,558,6,578,593,559,570,571,572,573,574,575,568,569,566,564,565,567,666,664,667,665,190,218,238,247,191,216,239,248,189,217,237,246,186,221,234,250,187,219,235,251,188,220,236,249,181,224,229,245,182,222,230,243,180,223,228,244,227,184,232,241,225,185,233,242,183,226,231,240,648,649,650,651,652,653,654,655,658,656,657,659,685,687,684,686,43,90,52,60,44,91,53,61,42,92,51,62,46,93,48,63,47,94,49,64,45,95,50,65,41,88,58,66,39,89,59,67,40,87,57,68,84,37,54,69,85,38,55,70,36,86,56,71,83,81,82,79,80,78,74,72,76,77,75,73,700,703,701,702,117,459,474,491,118,460,475,489,119,461,476,490,116,458,477,487,114,456,478,488,115,457,479,486,108,465,472,482,109,466,473,480,110,467,471,481,464,111,468,485,462,112,469,483,113,463,470,484,446,444,445,449,447,448,452,450,454,455,453,451,688,691,689,690,104,336,308,318,102,337,306,319,103,338,307,320,107,339,311,321,105,340,309,322,106,341,310,323,99,342,303,316,100,343,304,317,101,344,305,315,345,98,302,312,346,96,300,313,97,347,301,314,333,334,335,332,330,331,324,325,329,327,328,326,662,660,663,661,130,535,493,507,131,536,494,508,129,534,492,509,126,538,496,506,127,539,497,504,128,537,495,505,121,533,499,513,122,531,500,514,120,532,498,515,529,124,502,512,530,125,503,510,123,528,501,511,522,523,524,525,526,527,520,521,518,516,517,519,694,692,695,693,203,277,292,253,201,278,293,254,202,276,291,252,199,280,288,256,200,281,289,257,198,279,290,255,194,283,298,259,192,284,299,260,193,282,297,258,286,197,294,262,287,195,295,263,196,285,296,261,269,267,268,265,266,264,275,273,270,271,272,274,681,683,680,682,540,172,135,151,541,173,136,152,542,171,137,150,543,168,134,154,544,169,132,155,545,170,133,153,546,178,141,149,547,179,142,147,548,177,143,148,174,549,140,145,175,550,138,146,551,176,139,144,159,160,161,158,156,157,165,166,163,164,162,167,697,696,699,698,33,632,642,603,34,630,643,604,35,631,644,605,32,635,645,602,30,633,646,600,31,634,647,601,24,627,640,609,25,628,641,610,26,629,639,611,626,27,636,608,624,28,637,606,29,625,638,607,618,619,620,621,622,623,616,617,614,612,613,615,671,669,670,668,17,350,369,374,15,348,370,372,16,349,371,373,13,353,368,377,14,351,366,375,12,352,367,376,23,356,360,380,21,354,361,378,22,355,362,379,359,19,363,383,357,20,364,381,18,358,365,382,394,395,393,390,391,392,385,386,387,388,389,384,676,679,677,678 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#bef86252e34aac6c2a18a1e8b323957fca09c4d4a3c476c0116e0c729e633257, 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 20:32:19 · history