Equation 677 Database

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Magma b48c80eb0291…

magma b48c80eb0291
Size
381
Isomorphism class hash
b48c80eb029133ae906b2c315409b344640d69aff634ef78c8c8d00c28b24337
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 23:40:37
Display reorder
380,258,253,263,237,240,248,102,107,97,227,117,112,45,51,56,60,65,216,210,21,26,31,35,40,167,172,177,153,158,163,14,11,233,12,13,292,202,207,197,185,192,180,222,92,88,77,82,72,303,305,304,308,306,307,265,277,270,297,282,287,125,130,120,143,138,148,362,332,347,366,335,352,341,357,377,372,259,254,264,239,244,249,104,109,99,229,119,114,47,52,57,62,67,217,212,22,27,32,37,42,168,173,178,150,155,160,15,16,234,17,18,293,203,208,198,188,193,183,224,94,89,79,84,74,323,321,318,300,302,301,266,276,272,295,281,285,128,131,123,141,136,145,363,333,349,365,337,354,342,358,379,373,257,251,261,235,243,246,101,106,95,226,115,110,49,54,59,64,69,219,214,24,29,34,39,44,166,171,176,151,156,161,3,4,230,0,2,291,201,206,196,186,190,181,220,90,87,76,81,71,314,313,312,310,311,309,268,278,273,298,283,288,126,132,121,140,135,146,361,331,345,367,339,351,344,355,376,370,255,250,260,236,241,245,100,105,96,225,116,111,48,53,58,63,68,218,213,23,28,33,38,43,169,174,179,154,159,164,10,9,232,8,19,294,204,209,199,189,194,184,221,91,86,75,80,70,316,315,317,320,322,319,269,279,274,299,284,289,129,133,124,144,139,149,364,334,346,368,338,350,343,359,378,374,256,252,262,238,242,247,103,108,98,228,118,113,46,50,55,61,66,215,211,20,25,30,36,41,165,170,175,152,157,162,7,1,231,5,6,290,200,205,195,187,191,182,223,93,85,78,83,73,328,327,329,324,325,326,267,275,271,296,280,286,127,134,122,142,137,147,360,330,348,369,336,353,340,356,375,371 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#b1a8d3ba3db58654b282150679ccf1b928926281c9ba708fe38c950723e6a1aa, M = {70} 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 23:40:38 · history