Equation 677 Database

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Magma eca2972b9b98…

magma eca2972b9b98
Size
399
Isomorphism class hash
eca2972b9b9802715be2470b2c395848ad4b17816a2a5419455dbc2afdd9dca6
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 398) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-07 21:38:14
Display reorder
62,54,55,56,57,58,59,60,61,71,63,64,65,66,67,68,69,70,381,135,24,1,46,136,25,0,47,137,26,2,48,138,18,3,49,139,19,4,50,140,20,5,51,141,21,6,52,142,22,7,53,143,23,8,45,33,9,128,39,34,10,129,40,35,11,130,41,27,12,131,42,28,13,132,43,29,14,133,44,30,15,134,36,31,16,126,37,32,17,127,38,392,386,385,391,253,123,299,333,254,124,300,334,255,125,301,335,256,117,302,336,257,118,303,337,258,119,304,338,259,120,305,339,260,121,297,340,252,122,298,341,116,292,262,326,108,293,263,327,109,294,264,328,110,295,265,329,111,296,266,330,112,288,267,331,113,289,268,332,114,290,269,324,115,291,261,325,384,390,389,383,237,174,306,281,238,175,307,282,239,176,308,283,240,177,309,284,241,178,310,285,242,179,311,286,234,171,312,287,235,172,313,279,236,173,314,280,167,315,246,274,168,316,247,275,169,317,248,276,170,318,249,277,162,319,250,278,163,320,251,270,164,321,243,271,165,322,244,272,166,323,245,273,387,398,397,388,155,221,349,342,156,222,351,344,157,223,353,346,158,224,355,348,159,216,357,350,160,217,359,352,161,218,343,354,153,219,345,356,154,220,347,358,230,367,148,360,231,369,149,362,232,371,150,364,233,373,151,366,225,375,152,368,226,376,144,370,227,361,145,372,228,363,146,374,229,365,147,377,393,395,396,394,72,96,190,199,73,97,191,200,74,98,192,201,75,90,193,202,76,91,194,203,77,92,195,204,78,93,196,205,79,94,197,206,80,95,189,198,105,183,81,208,106,184,82,209,107,185,83,210,99,186,84,211,100,187,85,212,101,188,86,213,102,180,87,214,103,181,88,215,104,182,89,207,380,382,378,379 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 399 = 19 + 5*76, 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#0a9d5309e561d9925034107639b7a432af9b3bf2328c16207164bb790de1689c, M = the submagma generated by {0} (19 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, 76): MacNeish's product over GF(4) x GF(19); GF(4) = F_2[x]/(x^2 + 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: 21.

last edited by qawbecrdtey at 2026-10-07 21:38:15 · history