Equation 677 Database

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Magma 550038c6c137…

magma 550038c6c137
Size
381
Isomorphism class hash
550038c6c1377a3263289a598495f7ec4635bde2026b8ec23a02a4818c970073
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 23:30:49
Display reorder
380,110,160,180,131,122,170,192,142,125,175,166,115,145,45,96,196,246,320,317,318,136,186,106,155,151,201,9,1,211,261,231,281,81,30,20,76,270,220,242,292,42,92,71,26,225,275,215,265,66,15,296,321,319,51,36,85,235,285,10,205,61,255,251,100,55,322,361,345,350,341,365,355,377,335,371,331,111,161,183,133,120,172,191,140,127,177,165,116,147,47,97,197,247,307,310,308,138,188,105,156,150,200,6,0,210,260,233,283,83,33,21,77,272,222,240,290,41,90,72,27,227,277,216,266,65,16,297,329,309,50,38,88,238,288,11,206,60,256,250,101,56,306,363,346,352,340,368,357,376,336,372,330,113,163,182,132,123,173,190,141,128,178,168,118,146,46,95,195,245,316,313,311,135,185,108,158,153,203,7,3,213,263,232,282,82,32,23,78,273,223,241,291,40,91,73,28,228,278,218,268,68,18,295,314,312,53,35,86,236,286,13,208,63,258,252,103,58,315,362,348,353,343,366,358,375,338,370,333,112,162,181,130,121,171,193,143,126,176,167,117,148,48,98,198,248,326,323,324,137,187,107,157,152,202,5,2,212,262,230,280,80,31,22,75,271,221,243,293,43,93,70,25,226,276,217,267,67,17,298,327,325,52,37,87,237,287,12,207,62,257,254,102,57,328,360,347,351,342,367,356,378,337,373,332,114,164,184,134,124,174,194,144,129,179,169,119,149,49,99,199,249,304,300,302,139,189,109,159,154,204,8,4,214,264,234,284,84,34,24,79,274,224,244,294,44,94,74,29,229,279,219,269,69,19,299,305,301,54,39,89,239,289,14,209,64,259,253,104,59,303,364,349,354,344,369,359,379,339,374,334 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 = {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 23:30:50 · history