Equation 677 Database

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Magma 3332ab78f9c8…

magma 3332ab78f9c8
Size
381
Isomorphism class hash
3332ab78f9c8b0d56a9fdb973f09a1c59ce376a1b03e89608bf00e70c02957be
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 23:30:39
Display reorder
380,325,16,3,11,2,25,12,29,7,20,323,17,4,9,1,26,13,27,8,18,19,15,324,5,10,0,24,14,28,6,59,50,37,328,55,32,51,46,33,41,57,48,39,38,326,56,30,52,47,34,49,58,40,36,327,54,31,53,45,35,44,42,22,23,21,43,368,359,355,358,370,376,357,337,356,369,315,284,271,276,267,293,280,294,275,285,316,282,272,277,268,291,281,298,273,286,287,283,314,270,278,269,292,279,297,274,254,295,263,312,250,255,246,244,259,264,252,296,265,261,313,251,256,247,245,260,299,253,266,262,311,249,257,248,243,258,242,240,290,288,289,241,336,349,351,375,354,352,335,350,367,353,303,135,125,130,121,144,134,148,126,139,304,136,123,131,122,145,132,149,127,140,138,137,305,124,129,120,146,133,147,128,178,169,156,301,174,151,173,165,155,160,179,170,161,157,300,175,152,171,166,153,168,177,159,158,302,176,150,172,167,154,163,164,141,142,143,162,338,339,363,361,360,371,372,362,333,378,307,117,107,112,63,68,116,67,108,101,308,118,60,113,64,69,114,65,109,102,103,119,309,61,111,62,70,115,66,110,89,80,98,310,88,93,84,79,97,105,90,81,106,99,306,86,94,85,77,95,82,91,104,100,329,87,92,83,78,96,74,75,73,71,72,76,366,348,334,347,345,374,346,330,343,344,319,206,193,198,189,184,202,188,197,207,317,204,194,199,190,185,203,186,195,208,209,205,318,192,200,191,183,201,187,196,218,237,227,322,214,219,210,236,223,228,216,238,229,225,320,215,220,211,234,224,239,217,230,226,321,213,221,212,235,222,231,232,181,182,180,233,373,365,342,341,340,332,364,331,379,377 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#750328f1a2990ffd7db07d783e80f02cf584ad72d1ba7ccb23b4ce19aeead26b, 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 23:30:40 · history