Equation 677 Database

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Magma b3274d11c943…

magma b3274d11c943
Size
381
Isomorphism class hash
b3274d11c943061272ae717e274cc709f22bc1171178fb6035ec73d9cf3b1458
Satisfies Equation 255
yes
Right-cancellative
no
Idempotent
no
Fiber matrix
symmetric: no · normal: no · rank: 331 (nullity 50) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 23:40:04
Display reorder
380,12,171,23,145,252,13,253,172,18,144,173,254,14,19,146,255,168,15,20,149,256,169,16,21,147,257,170,17,22,148,310,166,81,102,229,325,167,82,103,230,311,162,83,104,231,309,163,78,105,232,326,164,79,106,233,323,165,80,107,228,296,298,299,295,294,297,362,345,338,366,350,352,355,368,348,369,63,262,108,85,280,64,281,263,109,86,258,276,65,110,87,277,259,60,111,88,278,260,61,112,89,279,261,62,113,84,314,211,2,128,151,317,212,3,129,150,324,213,4,126,152,312,214,5,130,153,328,215,1,131,154,313,210,0,127,155,237,239,234,235,236,238,371,337,331,357,330,341,365,361,339,363,119,270,122,7,216,115,217,271,123,8,272,218,114,124,9,219,273,116,125,10,220,275,117,121,11,221,274,118,120,6,320,267,36,70,190,321,269,37,71,191,329,266,38,66,186,318,265,39,67,187,327,264,40,68,188,319,268,41,69,189,159,161,156,157,158,160,356,342,351,358,333,335,359,367,336,360,76,247,100,95,285,77,286,248,97,90,250,287,72,99,91,283,246,73,101,92,282,249,74,96,93,284,251,75,98,94,315,224,42,135,194,316,225,43,137,195,305,226,44,136,196,306,227,45,132,197,307,222,46,134,192,322,223,47,133,193,245,241,242,243,244,240,376,340,347,374,344,332,372,364,353,370,142,199,53,25,205,143,206,200,48,26,201,207,138,49,27,208,202,139,50,28,209,203,140,51,29,204,198,141,52,24,300,293,35,59,181,308,292,30,54,182,302,288,31,55,183,303,289,32,56,184,304,290,33,57,185,301,291,34,58,180,175,177,178,179,174,176,379,354,349,375,346,334,378,377,343,373 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#abfe5bd49b6e166543faaec4df73d2086c367caff8baf8fe4b4ff03e493b773e, 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 23:40:05 · history