Equation 677 Database

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Magma 233b6b35a596…

magma 233b6b35a596
Size
381
Isomorphism class hash
233b6b35a596689341ec6d99f841464162332ddd5217f3504902039e19fd8df3
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 23:25:58
Display reorder
380,205,201,210,215,191,196,65,252,262,272,282,292,54,55,56,57,58,53,327,328,323,324,325,326,151,156,130,135,141,146,230,235,240,245,221,225,161,166,170,175,180,185,67,68,69,70,71,66,60,61,62,63,64,59,295,0,256,265,275,285,74,76,72,75,77,73,358,350,333,342,343,366,372,375,338,362,209,203,214,219,193,198,34,250,260,270,280,290,16,17,18,19,20,21,319,320,321,318,329,322,154,159,134,138,144,149,234,239,244,249,223,229,164,168,174,179,184,189,11,12,13,14,15,10,31,32,33,28,29,30,299,128,258,269,279,289,25,27,23,26,22,24,357,354,339,341,340,369,370,379,334,360,206,200,211,216,190,195,96,253,263,273,283,293,81,82,83,78,79,80,305,301,300,302,303,304,150,155,131,136,140,145,231,236,241,246,220,226,160,165,171,176,181,186,100,101,102,97,98,99,95,90,91,92,93,94,296,1,255,266,276,286,89,85,87,84,86,88,359,353,331,330,344,367,373,376,337,363,208,204,213,218,194,199,109,254,264,274,284,294,104,105,106,107,108,103,309,310,311,306,307,308,153,158,133,139,143,148,233,238,243,248,224,228,163,169,173,178,183,188,111,112,113,114,115,110,124,125,126,127,122,123,298,129,259,268,278,288,118,120,116,119,121,117,355,351,347,345,346,368,374,378,348,364,207,202,212,217,192,197,9,251,261,271,281,291,43,44,45,46,41,42,315,316,317,312,313,314,152,157,132,137,142,147,232,237,242,247,222,227,162,167,172,177,182,187,39,40,35,36,37,38,6,7,8,3,4,5,297,2,257,267,277,287,48,50,52,49,51,47,356,352,332,336,335,365,371,377,349,361 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#50609e522fd5f79e53ac56beafcb5b424f2d261582798854b4ac2a2a84486b65, 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 23:25:59 · history