Equation 677 Database

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Magma b3ac0a1689a0…

magma b3ac0a1689a0
Size
381
Isomorphism class hash
b3ac0a1689a0d64d4ae91b4fa0fb904bf256e01f235b244ac8d5bbfeb07c829d
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 23:41:28
Display reorder
380,111,110,112,113,108,109,132,133,134,135,136,137,28,29,24,25,26,27,216,226,236,186,196,206,140,141,142,143,138,139,207,217,227,237,187,197,31,32,33,34,35,30,267,277,289,297,247,257,117,118,119,114,115,116,266,276,286,296,246,256,311,307,308,310,309,306,348,349,352,353,365,334,376,364,335,377,64,63,65,60,61,62,102,103,104,105,106,107,87,88,89,84,85,86,219,229,239,189,199,209,101,96,97,98,99,100,203,213,223,233,183,193,92,93,94,95,90,91,263,273,283,293,243,253,71,66,67,68,69,70,269,279,288,299,249,259,326,328,329,325,324,327,341,340,346,347,360,344,379,368,345,374,14,13,15,16,17,12,164,165,166,167,162,163,9,10,11,6,7,8,210,220,230,181,191,200,158,159,160,161,156,157,208,218,228,238,188,198,2,3,4,5,1,0,268,278,287,298,248,258,22,23,18,19,20,21,261,271,281,290,241,251,323,319,320,322,321,318,333,332,356,357,366,331,372,362,330,378,176,175,177,178,179,174,54,55,56,57,58,59,79,80,81,82,83,78,214,224,234,184,194,204,53,48,49,50,51,52,205,215,225,235,185,195,76,77,72,73,74,75,265,275,285,295,245,255,171,172,173,168,169,170,264,274,284,294,244,254,312,314,315,317,316,313,358,359,338,339,363,343,370,361,342,375,42,47,43,44,45,46,149,144,145,146,147,148,120,121,122,123,124,125,212,222,232,182,192,202,154,155,150,151,152,153,201,211,221,231,180,190,130,131,126,127,128,129,260,270,280,291,240,250,40,41,36,37,38,39,262,272,282,292,242,252,304,301,300,303,302,305,336,337,355,354,369,350,373,367,351,371 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#b66edbbdcc18ab822aeb8c0e517cc0500614bfcd68d760a94b6b8cc01b086dc5, 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 23:41:29 · history