Equation 677 Database

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Magma eab601e84de1…

magma eab601e84de1
Size
381
Isomorphism class hash
eab601e84de1782d2169b2575ae55d928e05c2d73ce736f2c950ffb0e038b618
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 23:31:28
Display reorder
380,58,23,168,163,138,21,128,123,235,258,48,42,183,188,178,203,193,213,228,233,83,88,98,19,319,320,322,63,273,22,298,173,158,153,143,148,20,293,288,133,113,118,248,240,263,253,268,53,38,33,198,218,223,68,73,78,278,93,103,283,108,18,318,321,323,208,368,338,363,343,348,333,359,352,378,373,56,8,165,160,135,15,126,120,236,257,45,44,181,186,176,201,190,210,226,231,80,86,95,5,313,314,316,60,271,9,296,170,155,150,140,146,14,290,285,131,110,115,245,241,262,252,266,50,36,31,195,215,221,65,71,75,275,91,101,280,106,4,312,315,317,205,366,336,360,341,345,332,355,350,375,371,57,13,166,161,136,0,125,121,238,255,47,41,180,185,175,200,191,211,225,230,81,85,96,2,308,306,311,62,272,12,295,171,156,151,141,145,1,291,286,130,111,116,247,243,260,250,267,52,37,32,196,216,220,67,70,76,276,90,100,281,105,3,307,310,309,206,365,337,361,342,346,330,356,351,376,370,55,11,167,162,137,17,127,122,237,256,46,40,182,187,177,202,192,212,227,232,82,87,97,6,304,305,300,61,270,10,297,172,157,152,142,147,16,292,287,132,112,117,246,242,261,251,265,51,35,30,197,217,222,66,72,77,277,92,102,282,107,7,303,301,302,207,367,335,362,340,347,331,357,353,377,372,59,25,169,164,139,29,129,124,239,259,49,43,184,189,179,204,194,214,229,234,84,89,99,26,325,326,328,64,274,24,299,174,159,154,144,149,28,294,289,134,114,119,249,244,264,254,269,54,39,34,199,219,224,69,74,79,279,94,104,284,109,27,324,327,329,209,369,339,364,344,349,334,358,354,379,374 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#75c864f1b3b5ca4c55a580191a279ecc912d7e894cd469271a5b5b9ceed20bb0, M = {75} 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 23:31:29 · history