Equation 677 Database

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Magma 736775f33351…

magma 736775f33351
Size
381
Isomorphism class hash
736775f3335111c62ab31e0075c475bf7190e80a670258e15756579305d50ac0
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 23:19:16
Display reorder
380,12,114,13,14,94,104,279,289,299,249,259,269,44,19,24,29,34,39,274,284,294,244,254,264,59,64,69,74,49,54,224,234,184,194,204,214,229,239,189,199,209,219,124,134,144,154,164,174,313,314,315,316,317,312,139,149,159,169,179,129,89,84,79,99,109,119,332,350,355,333,377,344,370,346,362,367,3,111,4,5,91,101,276,285,295,246,256,266,41,16,21,26,31,36,271,281,291,240,250,260,58,63,68,73,48,53,220,230,180,190,200,210,225,237,187,195,205,215,120,130,140,150,161,171,327,328,329,324,325,326,136,146,155,165,175,126,85,80,75,96,106,116,336,351,358,341,378,340,371,349,364,368,10,113,11,9,93,103,278,288,298,248,258,268,43,18,23,28,33,38,273,283,293,243,253,263,55,60,65,70,46,50,221,231,181,191,201,211,228,238,188,197,208,218,121,131,141,151,160,170,302,303,304,305,301,300,138,148,158,168,178,128,88,83,78,98,108,118,338,353,357,331,379,343,374,348,363,369,1,110,0,2,90,100,275,286,296,245,255,265,40,15,20,25,30,35,272,282,292,242,252,262,57,62,67,72,47,52,222,232,182,192,202,212,226,236,186,198,206,216,122,132,142,152,162,172,309,310,311,306,307,308,135,145,156,166,176,125,86,81,76,95,105,115,330,352,359,335,376,339,372,345,361,366,7,112,8,6,92,102,277,287,297,247,257,267,42,17,22,27,32,37,270,280,290,241,251,261,56,61,66,71,45,51,223,233,183,193,203,213,227,235,185,196,207,217,123,133,143,153,163,173,320,321,322,323,318,319,137,147,157,167,177,127,87,82,77,97,107,117,337,354,356,334,375,342,373,347,360,365 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 = {71} 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 23:19:17 · history