Equation 677 Database

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Magma e30ec5ebffc4…

magma e30ec5ebffc4
Size
381
Isomorphism class hash
e30ec5ebffc41fa9928eb48a7933dc64616c993cb79f2f9a7e3212975e049cab
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 23:40:25
Display reorder
380,20,18,13,33,268,28,263,253,258,248,238,243,113,118,123,103,288,108,71,60,68,58,53,278,153,158,298,168,173,163,128,293,133,135,143,145,313,314,312,316,317,315,6,273,7,43,48,38,228,223,233,208,213,218,93,88,98,283,78,83,188,178,183,203,198,193,367,343,353,373,348,332,358,363,338,378,22,17,12,32,267,27,261,252,257,247,236,241,111,117,121,100,286,106,72,62,66,55,50,276,150,157,297,165,170,160,126,290,131,137,141,147,328,329,327,325,326,324,5,272,4,42,47,37,225,221,230,206,211,216,91,86,95,281,75,80,185,176,180,202,196,191,365,342,351,370,346,331,356,360,337,376,21,16,11,30,266,25,260,250,255,245,235,240,112,116,122,101,285,107,70,61,65,56,51,275,151,156,295,166,171,162,125,291,130,136,140,146,321,322,323,318,319,320,3,270,2,41,45,36,227,222,232,207,212,217,90,85,96,280,76,81,186,175,181,201,197,192,369,340,350,371,345,333,355,361,336,375,23,19,14,34,269,29,264,254,259,249,239,244,114,119,124,104,289,109,74,64,69,59,54,279,154,159,299,169,174,164,129,294,134,139,144,149,309,310,311,306,307,308,9,274,8,44,49,39,229,224,234,209,214,219,94,89,99,284,79,84,189,179,184,204,199,194,368,344,354,374,349,334,359,364,339,379,24,15,10,31,265,26,262,251,256,246,237,242,110,115,120,102,287,105,73,63,67,57,52,277,152,155,296,167,172,161,127,292,132,138,142,148,305,303,304,302,301,300,1,271,0,40,46,35,226,220,231,205,210,215,92,87,97,282,77,82,187,177,182,200,195,190,366,341,352,372,347,330,357,362,335,377 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 = {67} 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 23:40:26 · history