Equation 677 Database

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Magma 9cdda78e3674…

magma 9cdda78e3674
Size
381
Isomorphism class hash
9cdda78e3674b85a61dba82b645982a92ed0b5138c33fcb7417eab74988cb561
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 23:20:36
Display reorder
380,157,156,158,159,160,161,279,299,199,219,239,259,316,317,312,313,314,315,225,243,263,282,183,203,153,154,155,150,151,152,162,163,164,165,166,167,3,4,5,1,0,2,288,198,218,238,255,275,144,145,146,147,148,149,6,7,8,9,10,11,196,216,237,256,277,297,366,331,355,363,369,379,330,356,354,357,110,109,111,112,113,108,278,298,197,217,220,257,307,308,309,310,311,306,228,246,266,291,186,206,105,106,107,102,103,104,115,116,117,118,119,114,131,126,127,128,129,130,280,180,202,224,242,262,96,97,98,99,100,101,120,121,122,123,124,125,187,207,229,247,267,284,376,350,347,367,372,364,351,348,346,349,177,176,178,179,174,175,271,293,191,211,233,251,301,300,302,303,304,305,230,248,268,285,188,208,94,95,90,91,92,93,168,169,170,171,172,173,140,141,142,143,138,139,292,190,210,232,250,270,85,86,87,88,89,84,135,136,137,132,133,134,189,209,231,249,269,286,371,352,345,370,373,374,353,359,344,358,30,35,31,32,33,34,272,294,192,212,234,252,322,323,318,319,320,321,222,240,260,289,181,201,44,45,46,47,42,43,27,28,29,24,25,26,69,70,71,66,67,68,287,193,213,235,253,273,41,36,37,38,39,40,64,65,60,61,62,63,182,200,223,241,261,281,368,340,337,375,365,362,341,335,336,334,72,77,73,74,75,76,274,295,194,214,236,254,328,329,324,325,326,327,226,244,264,290,184,204,15,16,17,12,13,14,83,78,79,80,81,82,56,57,58,59,54,55,296,195,215,221,258,276,20,21,22,23,18,19,51,52,53,48,49,50,185,205,227,245,265,283,360,338,332,361,378,377,339,342,333,343 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#3136fd46544160d7110a12defb5eea5a4c1d4e69d8e8a4280fa062cfc3b165d6, M = {67} 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 23:20:38 · history