Equation 677 Database

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Magma c12448f05e0e…

magma c12448f05e0e
Size
381
Isomorphism class hash
c12448f05e0ea3dd2db60e9253b135ede8d93a66dd4e10b7817bead85464dbd5
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 23:24:50
Display reorder
380,308,307,309,310,311,306,11,16,21,26,0,5,150,155,161,166,171,176,126,131,136,141,146,120,60,65,70,76,81,86,291,296,271,276,281,286,256,261,266,240,246,251,216,221,226,231,236,210,206,180,185,191,196,201,116,95,111,101,106,90,40,50,35,56,30,45,344,377,347,374,335,366,361,359,339,340,301,305,300,302,303,304,13,18,23,29,4,8,154,159,164,169,174,179,128,134,139,144,148,123,64,69,74,79,83,89,294,299,274,279,283,288,259,264,268,243,248,254,218,224,229,234,238,213,208,183,189,194,198,203,118,99,113,104,108,93,43,53,38,58,33,49,330,376,353,371,350,369,364,355,338,352,322,321,323,318,319,320,12,17,22,27,2,7,153,158,163,168,173,178,127,132,137,142,147,122,62,67,72,77,82,87,292,297,272,277,282,287,257,262,267,242,247,252,217,222,227,232,237,212,207,182,187,192,197,202,117,97,112,102,107,92,42,52,37,57,32,47,346,379,341,373,345,367,360,358,337,336,315,314,316,317,312,313,14,19,24,28,3,9,151,156,160,165,170,175,129,133,138,143,149,124,63,68,73,78,84,88,293,298,273,278,284,289,258,263,269,244,249,253,219,223,228,233,239,214,209,184,188,193,199,204,119,98,114,103,109,94,44,54,39,59,34,48,349,378,354,372,348,368,363,356,342,351,329,328,324,325,326,327,10,15,20,25,1,6,152,157,162,167,172,177,125,130,135,140,145,121,61,66,71,75,80,85,290,295,270,275,280,285,255,260,265,241,245,250,215,220,225,230,235,211,205,181,186,190,195,200,115,96,110,100,105,91,41,51,36,55,31,46,332,375,343,370,333,365,362,357,334,331 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#4ff69c35f55aa106c20b4528e074e3f72eddedd150e00069ea529e91bc9e2010, M = {76} 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 23:24:51 · history