Equation 677 Database

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Magma 6741ca2a79c3…

magma 6741ca2a79c3
Size
381
Isomorphism class hash
6741ca2a79c3f0d029709a1d875ae10c9cd43bab4f784b24483d298292d61bfa
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 23:23:30
Display reorder
380,212,253,103,29,2,3,213,254,104,24,214,4,255,105,25,256,5,215,106,26,1,257,210,107,27,252,0,211,102,28,154,91,323,62,243,92,155,324,63,244,93,151,325,64,245,94,150,326,65,240,95,152,329,60,241,90,153,322,61,242,175,177,178,179,174,176,356,347,371,341,368,367,337,344,353,361,262,232,82,69,97,98,263,233,83,70,258,99,228,78,71,229,100,259,79,66,101,230,260,80,67,231,96,261,81,68,249,45,314,110,195,46,250,300,111,196,47,251,301,112,197,42,246,327,113,192,43,247,302,108,193,44,248,321,109,194,221,217,218,219,220,216,369,336,365,342,372,358,345,348,338,366,166,158,8,149,122,123,167,159,9,144,162,124,160,10,145,161,125,163,11,146,121,156,164,6,147,157,120,165,7,148,275,115,318,14,265,116,274,319,15,266,117,270,328,16,267,118,271,315,17,268,119,272,316,12,269,114,273,317,13,264,297,298,299,294,296,295,363,346,370,351,373,360,331,349,343,359,288,238,86,39,54,55,290,239,87,40,291,56,234,88,41,235,57,292,89,36,58,236,293,84,37,237,59,289,85,38,206,128,305,138,278,129,207,306,140,281,130,208,307,143,280,131,209,304,141,279,127,204,303,139,276,126,205,320,142,277,191,187,188,189,190,186,362,332,375,340,374,357,330,352,334,355,283,181,35,19,76,77,284,182,30,20,285,72,183,31,21,184,73,282,32,22,74,185,286,33,23,180,75,287,34,18,222,48,309,133,198,49,223,310,134,199,50,224,311,135,200,51,225,312,136,201,52,226,313,137,202,53,227,308,132,203,169,171,172,173,168,170,376,354,379,333,377,364,335,339,350,378 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#49ff6987e56411c363e1f8e7c7cc0364a561ac711b930e65bd87af69aea47be0, 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 23:23:31 · history