Equation 677 Database

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Magma a6df46a3432d…

magma a6df46a3432d
Size
381
Isomorphism class hash
a6df46a3432d6087eed75f281feb49909cf897f54e2883d285de7cd2de7c16c3
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 23:31:06
Display reorder
380,17,74,44,24,147,136,164,189,214,204,254,279,127,117,122,102,107,64,49,54,327,325,239,229,87,92,77,284,18,19,34,39,289,29,152,157,131,142,169,174,179,184,209,219,194,199,259,264,274,269,112,69,59,16,328,329,326,324,244,234,249,224,97,82,297,294,334,339,357,368,349,354,344,377,371,364,10,72,41,20,148,138,162,187,212,202,251,276,128,118,123,103,108,61,46,51,305,301,237,227,88,93,78,282,9,8,31,36,285,25,153,158,133,143,167,172,177,182,207,217,192,197,256,262,270,265,113,66,55,11,303,304,300,302,242,232,247,222,98,83,298,291,331,336,358,367,347,352,342,378,372,361,4,70,42,22,146,137,161,185,211,200,252,277,126,115,120,101,105,60,45,50,309,307,236,225,86,91,76,281,5,6,32,37,287,27,151,156,132,141,165,170,176,180,206,215,191,196,257,261,272,267,110,65,56,3,310,311,308,306,241,230,246,220,96,80,295,290,332,337,355,365,345,351,341,375,370,360,7,71,40,21,145,135,160,186,210,201,250,275,125,116,121,100,106,62,47,52,315,313,235,226,85,90,75,280,2,1,30,35,286,26,150,155,130,140,166,171,175,181,205,216,190,195,255,260,271,266,111,67,57,0,316,317,314,312,240,231,245,221,95,81,296,292,330,335,356,366,346,350,340,376,374,362,14,73,43,23,149,139,163,188,213,203,253,278,129,119,124,104,109,63,48,53,321,319,238,228,89,94,79,283,13,12,33,38,288,28,154,159,134,144,168,173,178,183,208,218,193,198,258,263,273,268,114,68,58,15,322,323,320,318,243,233,248,223,99,84,299,293,333,338,359,369,348,353,343,379,373,363 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#75c864f1b3b5ca4c55a580191a279ecc912d7e894cd469271a5b5b9ceed20bb0, M = {70} 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 23:31:07 · history