Equation 677 Database

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Magma b6ede70395c9…

magma b6ede70395c9
Size
381
Isomorphism class hash
b6ede70395c92353c3f303e5261a88965dd9d385af8cf6c5e705620886ce1677
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 23:25:03
Display reorder
380,92,37,137,187,237,287,210,263,11,66,110,160,152,202,252,2,54,102,107,157,207,257,7,62,141,195,245,295,45,95,147,192,242,292,42,55,311,306,307,308,309,310,116,166,216,266,15,71,175,225,275,26,81,126,87,182,32,232,282,132,77,172,22,222,272,122,369,372,375,356,364,342,350,344,352,335,94,39,139,189,239,289,214,264,14,69,114,164,154,204,254,4,59,104,109,159,209,259,9,64,144,199,249,299,49,99,149,194,244,294,44,58,324,325,326,327,328,329,119,169,219,269,19,74,179,229,279,29,84,129,89,184,34,234,284,134,76,170,20,220,270,121,368,370,379,359,360,354,345,351,334,353,90,35,135,185,235,285,211,261,12,65,111,161,151,201,251,1,51,101,106,156,206,255,6,61,142,197,247,297,47,97,146,191,241,291,40,53,303,304,305,301,300,302,117,167,217,267,17,72,177,227,277,27,82,127,86,181,31,231,281,131,78,173,23,223,273,123,365,371,378,357,362,343,338,349,346,347,91,36,136,186,236,286,212,260,10,67,112,162,150,200,250,0,52,100,105,155,205,256,5,60,140,196,246,296,46,96,145,190,240,290,41,50,323,318,319,320,321,322,115,165,215,265,16,70,176,226,276,25,80,125,85,180,30,230,280,130,75,171,21,221,271,120,367,374,377,358,361,339,348,336,337,330,93,38,138,188,238,288,213,262,13,68,113,163,153,203,253,3,56,103,108,158,208,258,8,63,143,198,248,298,48,98,148,193,243,293,43,57,313,314,315,316,317,312,118,168,218,268,18,73,178,228,278,28,83,128,88,183,33,233,283,133,79,174,24,224,274,124,366,373,376,355,363,340,333,341,332,331 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 = {69} 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 23:25:04 · history