Equation 677 Database

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Magma ab101856e874…

magma ab101856e874
Size
381
Isomorphism class hash
ab101856e87424060837a0f6520d0539403f904dd24470f1dce5a32b5ffdcefe
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 380) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 23:50:49
Display reorder
380,241,24,23,21,22,20,286,231,236,225,215,220,315,316,317,312,313,314,283,83,88,92,98,103,146,135,140,131,121,126,28,210,27,25,26,271,156,161,151,170,176,165,268,278,263,253,255,246,196,201,206,180,185,190,62,294,63,113,118,108,19,18,17,295,16,15,355,335,361,331,346,376,368,353,343,370,240,2,3,4,5,6,285,230,235,226,216,221,308,306,307,311,309,310,280,81,86,94,95,101,145,136,141,130,120,125,7,211,29,30,31,270,155,160,150,171,175,166,266,276,261,250,256,245,195,200,205,181,186,191,1,291,0,111,116,105,11,10,12,296,8,9,356,336,360,330,345,375,365,351,340,371,242,45,44,42,43,41,287,232,237,227,217,222,305,303,304,302,301,300,281,80,85,91,96,100,147,137,142,132,122,127,35,212,32,33,34,272,157,162,152,172,177,167,265,275,260,251,257,247,197,202,207,182,187,192,14,290,13,110,115,106,40,37,36,297,38,39,357,337,362,332,347,377,366,350,341,372,243,61,60,59,57,58,288,233,238,228,218,223,328,329,327,325,326,324,282,82,87,90,97,102,148,138,143,133,123,128,48,213,49,50,51,273,158,163,153,173,178,168,267,277,262,252,258,248,198,203,208,183,188,193,47,292,46,112,117,107,52,53,56,298,54,55,358,338,363,333,348,378,367,352,342,373,244,76,75,79,77,78,289,234,239,229,219,224,320,318,319,323,321,322,284,84,89,93,99,104,149,139,144,134,124,129,69,214,66,67,68,274,159,164,154,174,179,169,269,279,264,254,259,249,199,204,209,184,189,194,65,293,64,114,119,109,72,71,70,299,74,73,359,339,364,334,349,379,369,354,344,374 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 381 = 1 + 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#fac090d670a9c14492c148fae382a21bad3e48687c67df8555101af0e65e1711, M = {68} 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: 51.

last edited by qawbecrdtey at 2026-10-01 23:50:49 · history