Equation 677 Database

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Magma 98c19c169b8b…

magma 98c19c169b8b
Size
595
Isomorphism class hash
98c19c169b8bb7209491b6f6ddc85b5b0b927e84a0af3137ec9ced1bf07a240d
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
2026-10-08 21:31:05
Display reorder
88,87,89,84,85,86,388,390,389,387,385,386,406,408,407,405,403,404,358,360,359,357,355,356,371,370,372,369,367,368,515,516,510,517,570,72,77,73,74,75,76,147,146,143,144,145,142,186,185,187,188,189,184,25,24,26,27,28,29,177,176,172,173,174,175,258,263,259,260,261,262,9,8,10,11,6,7,107,106,102,103,104,105,66,71,67,68,69,70,3,2,4,5,1,0,342,341,340,345,343,344,349,351,350,346,347,348,400,402,401,397,398,399,373,375,374,376,377,378,466,465,504,505,467,468,354,477,448,476,447,475,530,535,526,519,518,533,551,587,568,564,556,583,584,545,555,549,282,287,283,284,285,286,197,196,199,200,201,198,64,63,65,60,61,62,252,257,253,254,255,256,120,119,121,122,123,118,277,276,278,279,280,281,149,148,150,151,152,153,48,53,49,50,51,52,293,292,288,289,290,291,227,226,228,229,224,225,450,449,411,483,500,482,494,501,495,491,492,493,507,487,499,486,456,455,478,442,441,440,438,439,362,361,363,364,365,366,353,474,446,473,445,472,542,528,541,513,540,514,585,590,559,574,546,565,550,578,592,591,206,205,207,202,203,204,90,95,92,93,94,91,158,157,159,154,155,156,16,15,17,12,13,14,35,34,30,31,32,33,171,170,166,167,168,169,248,114,116,117,247,115,301,300,302,303,304,305,218,223,219,220,221,222,195,194,190,191,192,193,380,379,381,383,384,382,317,319,318,320,321,322,324,323,325,327,328,326,395,394,396,392,393,391,490,489,509,412,508,488,479,409,480,506,481,410,536,537,512,524,511,527,544,567,552,572,594,558,569,573,577,575,23,22,18,19,20,21,208,249,210,211,250,209,178,183,179,180,181,182,217,216,212,213,214,215,239,238,240,241,236,237,133,132,134,135,130,131,101,100,96,97,98,99,275,274,270,271,272,273,79,78,80,81,82,83,37,36,38,39,40,41,462,427,426,315,313,314,336,335,334,339,337,338,332,331,333,329,330,437,430,464,316,463,428,429,310,312,311,309,307,308,422,420,502,498,503,421,521,532,534,522,523,543,579,580,581,576,589,554,571,557,553,547,129,128,124,125,126,127,245,244,251,242,243,246,267,266,268,269,264,265,141,140,136,137,138,139,56,55,57,58,59,54,109,108,110,111,112,113,298,297,299,294,295,296,43,42,44,45,46,47,230,235,231,232,233,234,161,160,162,163,164,165,485,453,454,451,452,484,496,459,458,419,457,497,436,435,434,433,431,432,425,461,306,460,424,423,417,416,418,413,414,415,352,471,444,469,443,470,539,538,525,520,531,529,563,561,548,582,560,593,588,566,586,562 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#40b1db721c17bf32e266eb97cd1492697125779c7804a195f580e3a793b1a85e, M = the submagma generated by {18, 90} (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 2026-10-08 21:31:06 · history