Equation 677 Database

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Magma 4b83f3768c33…

magma 4b83f3768c33
Size
381
Isomorphism class hash
4b83f3768c3359a5faa459fe56e10adc186fd584439cc458d3906810f51a8c0f
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 23:19:20
Display reorder
380,265,260,271,276,250,255,185,281,295,170,175,180,22,27,32,37,42,47,106,81,86,91,96,100,329,324,325,326,327,328,52,57,62,67,72,77,205,210,215,191,195,200,160,165,140,145,150,155,221,225,230,235,240,245,122,127,132,137,112,117,10,9,11,287,292,8,335,352,345,373,341,359,334,375,365,362,266,261,270,275,251,256,186,280,296,171,176,181,21,25,30,35,40,45,105,80,85,90,95,101,300,302,303,304,305,301,50,55,60,66,71,76,206,211,216,190,196,201,161,166,141,146,151,156,220,226,231,236,241,246,123,128,133,138,113,118,3,2,1,285,290,0,339,353,348,372,340,358,332,376,366,361,267,262,273,277,252,257,187,282,297,172,177,182,23,28,33,38,43,48,107,82,87,92,97,102,318,319,320,321,322,323,53,58,63,68,73,78,207,212,217,192,197,202,162,167,142,147,152,157,222,227,232,237,242,247,121,126,131,135,111,116,12,15,13,288,293,14,336,351,347,370,343,355,330,377,367,360,268,263,272,278,253,258,188,283,298,173,178,183,20,26,31,36,41,46,108,83,88,93,98,103,317,312,313,314,315,316,51,56,61,65,70,75,208,213,218,193,198,203,163,168,143,148,153,158,223,228,233,238,243,248,124,129,134,139,114,119,18,17,19,289,294,16,338,350,349,371,342,356,333,378,368,364,269,264,274,279,254,259,189,284,299,174,179,184,24,29,34,39,44,49,109,84,89,94,99,104,310,311,306,307,308,309,54,59,64,69,74,79,209,214,219,194,199,204,164,169,144,149,154,159,224,229,234,239,244,249,120,125,130,136,110,115,6,5,7,286,291,4,337,354,346,374,344,357,331,379,369,363 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#10cca86363523145d0eb290792d3d13154c9d146d7a7475a96ac2cf61ae39af6, M = {72} 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 23:19:21 · history