Equation 677 Database

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Magma 9fe91a74ff1c…

magma 9fe91a74ff1c
Size
595
Isomorphism class hash
9fe91a74ff1c754ec372429983b82416ae846d26485b59c80ccdcd98f2649c44
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 594) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-06 11:46:47
Display reorder
98,97,99,100,95,96,41,46,42,43,44,45,316,318,317,320,321,319,378,377,376,379,380,381,346,345,344,341,342,343,519,530,513,570,577,231,233,232,229,230,228,136,135,137,132,133,134,32,31,33,34,29,30,101,106,102,103,104,105,176,175,177,178,179,174,298,297,299,294,295,296,210,215,211,212,213,214,274,273,275,270,271,272,72,74,71,75,76,73,78,77,79,80,81,82,336,335,337,338,339,340,314,312,313,399,400,398,401,403,402,391,389,390,334,333,332,331,329,330,468,467,504,505,469,470,315,463,429,462,428,461,533,531,528,523,524,521,546,557,592,587,585,571,544,550,584,548,19,21,20,17,18,22,206,205,207,208,209,204,301,300,302,303,304,305,87,86,88,83,84,85,158,157,159,160,161,156,293,292,288,289,290,291,180,185,181,182,183,184,169,168,170,171,172,173,130,126,129,127,128,125,10,9,5,6,7,8,443,442,410,483,500,482,491,499,492,490,488,489,509,494,501,493,456,457,460,427,426,425,423,424,328,327,326,325,323,324,322,466,431,465,430,464,532,534,516,539,540,541,545,555,591,559,561,565,566,567,560,593,55,57,56,53,54,58,162,167,163,164,165,166,28,27,23,24,25,26,190,189,191,186,187,188,113,118,114,115,116,117,110,109,111,112,107,108,143,142,138,139,140,141,307,306,308,309,310,311,131,4,1,0,2,3,122,121,123,124,119,120,375,374,373,371,372,370,353,352,354,355,356,357,385,387,386,384,382,383,348,404,347,351,349,350,476,477,507,388,506,475,479,408,480,508,481,409,535,536,515,514,511,512,562,549,554,594,553,543,551,558,552,547,259,261,260,263,258,262,35,40,36,37,38,39,199,198,200,201,202,203,218,217,219,220,221,216,251,250,246,247,248,249,92,91,93,94,89,90,286,285,287,282,283,284,12,11,13,14,15,16,64,60,63,61,62,59,47,52,48,49,50,51,478,441,440,405,406,407,396,395,397,392,393,394,367,366,368,369,365,439,447,486,412,487,448,449,361,360,359,364,362,363,422,420,502,498,503,421,542,527,522,520,517,518,569,581,568,589,590,583,556,563,580,564,70,66,65,68,69,67,277,276,278,279,280,281,192,197,193,194,195,196,235,234,236,237,238,239,147,146,148,149,144,145,150,155,151,152,153,154,256,255,257,252,253,254,268,267,269,264,265,266,227,223,226,224,225,222,245,244,240,241,242,243,471,433,432,434,435,472,484,444,445,411,446,485,452,451,450,454,455,453,436,473,358,474,437,438,413,415,414,416,417,418,419,497,459,496,458,495,538,537,525,529,510,526,572,573,574,586,582,575,578,588,579,576 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 595 = 35 + 5*112, 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, 5, B) with E = magma#10d95f4d62da29d597cabb26c5d7a2889acb76e08f2897cdd164594c6bfbc5c4, M = the submagma generated by {48, 66} (35 elements) in E, B = magma#e549b5f8492c9b6b5ad530e3aa4f39c6e23d08645ebd1b36a3c2de2a5a23bac5. 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(5, 112): MacNeish's product over GF(16) x GF(7); GF(16) = F_2[x]/(x^4 + 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: 85.

last edited by qawbecrdtey at 2026-10-06 11:46:49 · history