Equation 677 Database

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Magma 9ec116c51153…

magma 9ec116c51153
Size
381
Isomorphism class hash
9ec116c51153eb7b5c7abf3d455447329bac9492c1decf263b923c05a48f2315
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 23:46:45
Display reorder
380,301,148,139,164,153,165,135,169,127,133,170,82,194,190,178,300,94,87,189,97,195,83,215,203,116,219,102,302,121,111,214,220,112,63,303,72,239,245,240,228,67,244,55,64,13,304,22,271,266,261,252,17,265,5,14,305,39,35,289,295,290,278,36,294,37,38,369,365,344,341,342,343,366,340,367,368,328,131,134,168,161,160,143,167,144,132,152,79,192,185,186,329,85,89,193,92,177,80,210,211,114,217,120,327,115,108,218,202,109,62,325,53,243,227,235,236,66,242,71,50,12,326,3,264,270,258,259,16,263,21,0,324,32,33,293,277,285,286,34,292,30,31,362,363,337,339,335,336,364,338,360,361,312,147,138,162,155,163,137,172,128,141,171,81,197,188,180,313,91,90,187,95,196,77,213,205,118,221,103,314,119,110,212,222,104,51,315,70,237,247,238,230,69,246,57,58,1,316,19,269,268,260,254,20,267,7,8,317,29,25,287,296,288,280,26,297,27,28,359,356,334,330,332,333,355,331,357,358,306,145,142,154,156,174,136,166,146,149,157,98,191,199,181,307,84,88,179,78,182,99,224,206,117,216,105,308,113,123,204,207,124,56,309,65,229,232,249,231,68,241,59,74,6,310,15,253,256,274,255,18,262,9,24,311,46,47,279,282,299,281,48,291,49,45,375,376,351,353,354,350,377,352,378,379,322,129,130,158,151,150,140,159,126,125,173,86,184,175,176,323,93,96,183,75,198,76,200,201,122,209,101,321,107,106,208,223,100,61,319,60,233,248,226,225,73,234,54,52,11,320,10,257,272,251,250,23,273,4,2,318,43,44,283,298,276,275,40,284,41,42,373,374,348,345,346,347,370,349,371,372 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#de65c3a27d2d103931ef27b8504dde23b1d68e34b289a9b4c0406a68fde57db8, 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 23:46:45 · history