Equation 677 Database

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Magma fff8cd175cb1…

magma fff8cd175cb1
Size
381
Isomorphism class hash
fff8cd175cb13bae32b28f587fa20ee03f01cd79c0984800909ed90a337a95f0
Satisfies Equation 255
yes
Right-cancellative
no
Idempotent
no
Fiber matrix
symmetric: no · normal: yes · rank: 301 (nullity 80) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 23:19:46
Display reorder
357,22,73,20,21,19,17,18,71,72,93,94,95,96,97,98,99,85,86,87,88,89,90,91,92,75,76,77,78,79,80,81,82,83,84,70,197,198,253,255,259,263,267,189,190,191,192,193,194,195,196,302,306,310,314,318,322,327,270,274,278,282,286,290,294,298,74,372,353,373,337,346,359,358,369,347,378,157,200,158,156,154,155,153,213,214,220,221,222,223,224,225,226,227,228,229,215,216,217,218,219,202,203,204,205,206,207,208,209,210,211,212,233,231,251,257,261,265,269,248,246,244,242,240,238,236,234,304,308,312,316,320,324,328,272,276,280,284,288,292,296,300,201,330,355,341,343,374,340,368,360,364,379,7,144,8,9,10,11,12,142,143,131,132,133,134,135,136,137,123,124,125,126,127,128,129,130,146,147,148,149,150,151,152,138,139,140,141,16,1,252,254,258,262,266,35,36,37,38,39,13,14,15,303,307,311,315,319,323,326,271,275,279,283,287,291,295,299,145,361,352,351,349,348,370,344,345,362,377,2,178,3,0,5,6,4,176,177,165,166,167,168,169,170,171,172,173,159,160,161,162,163,164,180,181,182,183,184,185,186,187,188,174,175,232,230,250,256,260,264,268,249,247,245,243,241,239,237,235,305,309,313,317,321,325,329,273,277,281,285,289,293,297,301,179,375,354,371,367,366,365,342,363,350,380,33,120,34,32,30,31,29,118,119,107,28,27,26,25,24,23,199,100,101,102,103,104,105,106,122,108,109,110,111,112,113,114,115,116,117,47,48,49,50,51,52,53,54,40,41,42,43,44,45,46,62,63,64,65,66,67,68,69,55,56,57,58,59,60,61,121,332,356,331,339,338,335,336,334,333,376 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#142468854d405b83c00226884d8f598ec4006f0ae2920d7a6c0d23cc63337a08, M = {66} 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 23:19:47 · history