Equation 677 Database

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Magma bed36b2c3df3…

magma bed36b2c3df3
Size
381
Isomorphism class hash
bed36b2c3df3ef351414c5eba29310472484e34bc36eb2c9b0c74f99299555c9
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 23:50:36
Display reorder
380,253,248,257,260,265,275,157,162,152,172,177,167,210,1,271,37,38,39,51,52,53,243,49,50,122,127,132,137,142,147,202,207,197,187,192,182,44,45,46,47,48,297,112,292,117,97,102,107,84,85,90,72,281,76,227,217,222,287,232,237,305,304,303,300,302,301,332,335,357,341,362,368,352,347,378,372,252,246,256,262,266,276,155,160,150,171,176,166,211,40,270,28,41,27,17,18,19,241,26,16,121,126,131,135,140,146,200,205,195,186,191,181,20,21,22,23,24,295,110,291,115,95,100,105,82,86,91,70,280,75,226,215,221,286,230,235,326,325,324,328,329,327,330,336,355,340,361,365,351,346,376,370,251,247,255,261,267,277,159,164,154,174,179,169,212,42,272,10,11,43,6,7,25,240,9,8,124,129,134,139,144,149,203,208,198,188,193,183,5,3,4,2,0,296,114,294,119,99,104,109,80,87,92,73,282,78,225,216,220,285,231,236,322,321,323,318,319,320,333,337,356,342,363,366,354,345,375,374,250,245,258,263,268,278,158,163,153,173,178,168,213,57,273,56,54,55,65,13,12,242,63,64,123,128,133,138,143,148,204,209,199,189,194,184,58,59,60,61,62,298,113,293,118,98,103,108,81,88,93,71,283,77,228,218,223,288,233,238,307,306,308,309,310,311,334,338,358,343,364,367,353,348,377,373,254,249,259,264,269,279,156,161,151,170,175,165,214,69,274,68,66,67,36,34,35,244,15,14,120,125,130,136,141,145,201,206,196,185,190,180,29,30,31,32,33,299,111,290,116,96,101,106,83,89,94,74,284,79,229,219,224,289,234,239,315,317,316,314,312,313,331,339,359,344,360,369,350,349,379,371 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 = {66} 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 23:50:37 · history