Equation 677 Database

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Magma 9dc717fc86ff…

magma 9dc717fc86ff
Size
381
Isomorphism class hash
9dc717fc86ffb381938a7deab8a9cddf936e5d60cb4dc056011461278a7280e5
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 23:25:07
Display reorder
380,285,280,290,295,271,276,225,230,235,211,215,220,136,141,146,121,126,131,46,51,56,31,36,41,170,175,150,155,160,165,110,115,90,95,100,105,255,260,265,241,245,250,81,86,61,66,71,76,11,6,7,8,9,10,327,329,326,324,325,328,190,200,186,205,181,195,363,355,338,371,376,335,343,368,349,352,288,283,293,299,273,278,228,233,239,213,218,223,139,144,149,123,128,133,48,54,59,34,38,43,174,179,153,158,164,169,114,119,93,98,103,108,258,263,269,243,248,253,84,89,63,68,73,79,24,26,28,19,21,22,319,321,318,322,323,320,193,204,188,209,183,199,364,358,339,374,379,333,332,369,345,350,287,282,292,297,272,277,227,232,237,212,217,222,137,142,147,122,127,132,47,52,57,32,37,42,172,177,152,157,162,167,112,117,92,97,102,107,257,262,267,242,247,252,82,87,62,67,72,77,12,13,14,15,16,17,302,304,300,305,301,303,192,202,187,207,182,197,361,359,347,372,375,342,348,366,346,353,289,284,294,298,274,279,229,234,238,214,219,224,138,143,148,124,129,134,49,53,58,33,39,44,173,178,154,159,163,168,113,118,94,99,104,109,259,264,268,244,249,254,83,88,64,69,74,78,25,27,29,18,20,23,308,310,307,311,306,309,194,203,189,208,184,198,362,357,334,373,378,336,331,365,330,351,286,281,291,296,270,275,226,231,236,210,216,221,135,140,145,120,125,130,45,50,55,30,35,40,171,176,151,156,161,166,111,116,91,96,101,106,256,261,266,240,246,251,80,85,60,65,70,75,4,5,1,0,2,3,314,316,313,317,312,315,191,201,185,206,180,196,360,356,337,370,377,344,341,367,340,354 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#4ff69c35f55aa106c20b4528e074e3f72eddedd150e00069ea529e91bc9e2010, 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 23:25:08 · history